Letter pubs.acs.org/NanoLett
Enhanced Electrical and Thermal Conduction in GrapheneEncapsulated Copper Nanowires Ruchit Mehta, Sunny Chugh, and Zhihong Chen* †
School of Electrical and Computer Engineering and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, United States S Supporting Information *
ABSTRACT: Highly conductive copper nanowires (CuNWs) are essential for efficient data transfer and heat conduction in wide ranging applications like high-performance semiconductor chips and transparent conductors. However, size scaling of CuNWs causes severe reduction in electrical and thermal conductivity due to substantial inelastic surface scattering of electrons. Here we report a novel scalable technique for lowtemperature deposition of graphene around CuNWs and observe strong enhancement of electrical and thermal conductivity for graphene-encapsulated CuNWs compared to uncoated CuNWs. Fitting the experimental data with the theoretical model for conductivity of CuNWs reveals significant reduction in surface scattering of electrons at the oxide-free CuNW surfaces, translating into 15% faster data transfer and 27% lower peak temperature compared to the same CuNW without the graphene coating. Our results provide compelling evidence for improved speed and thermal management by adapting the Cu−graphene hybrid technology in future ultrascaled silicon chips and air-stable flexible electronic applications. KEYWORDS: Graphene, copper nanowires, electrical conductivity, thermal conductivity, graphene−copper hybrids, low-temperature graphene deposition, plasma CVD
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coupling, resulting in complete inelastic scattering of electrons at the Cu−Ta interface.16 Limited current drive capacity and higher signal delays follow directly from the reduced conductivity in scaled CuNWs, causing major bottlenecks for future speed up of silicon chips.5 Additionally, increasing resistivity leads to significant heat generation in scaled CuNWs,3,17,18 which has deleterious effects on thermal management and reliability.18 So, it is of great interest to curb the rising resistivity of CuNWs and this Letter discusses a viable solution to this problem. Graphene is known to have remarkable in-plane stiffness19,20 to prevent mechanical deformation, impermeability21 to protect Cu against reactive chemical22 or gaseous23 species, along with low density-of-states to avoid perturbation of Cu surface potential after coating.24 All of these superior physical properties make graphene an ideal noninteracting barrier for CuNWs to prevent oxidation and interdiffusion. There are recent reports on the electrical and thermal benefits of graphene capping on large area Cu foils25 or micrometerscale Cu wires,26 however, these cannot be extended to nanometer-scaled Cu wires due to markedly different scattering phenomenon occurring in the nanoscale regime. Furthermore,
urface scattering is a phenomenon in which electrons impinging the surfaces of a nanowire (NW) undergo either elastic (specular) or inelastic (diffuse) scattering depending on the nature of the local surface states. For NW sizes close to the electron mean free path1 (40 nm in Cu at 298 K), a significant part of the total electron density locates near the NW surfaces. CuNWs are the material of choice for swift data transfer inside computer chips2−5 and efficient current flow in flexible transparent conductors.6−10 However, inelastic electron scattering at the surfaces of the CuNWs drastically reduces copper’s electrical and thermal conductivity below the bulk values.1,11,12 Having pristine CuNW surfaces can partially reduce inelastic scattering, but in real applications there is large modification of the pristine surface due to oxidation or other metallic coatings.13,14 For the use in flexible transparent conductors, CuNWs are usually exposed to ambient environment causing Cu oxide formation at the surfaces. Trap states at the Cu−Cu oxide interface lead to complete inelastic scattering through randomization of the electron momentum in the direction of current flow.13,15 On the other hand, Cu interconnects in silicon chips are embedded within dielectrics and care is taken to avoid surface oxidation during processing. Typically, these interconnects are surrounded by thin layers of tantalum (Ta) acting as Cu diffusion barriers.5,12 The complex Fermi surface of a high density-of-states metal like Ta perturbs the smooth surface potential of Cu and increases the interfacial electronic © XXXX American Chemical Society
Received: December 19, 2014 Revised: January 25, 2015
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DOI: 10.1021/nl504889t Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. Fabrication and characterization of Cu-graphene (Cu-G) hybrid NWs. (a) Schematic of a CuNW conformally coated with graphene. (b) Experimental scheme used in this work, starting with PECVD graphene deposition on as-fabricated CuNWs. The resulting hybrid NWs (Cu-G) were analyzed, followed by oxygen etching to obtain the same NWs without the graphene coating (Cu-NG). This scheme allows for a fair comparison of properties between Cu-G and Cu-NG NWs. (c) Scanning electron image of a 180 nm wide Cu-G NW. (d) Raman spectroscopy data, acquired using a 532 nm laser, showing the distinct graphene peaks on Cu-G samples while no graphene peaks are seen on Cu-NG and SiO2. (e) X-ray photoelectron spectrum (XPS) showing sp2 hybridized carbon orbitals of graphene in Cu-G samples. (f) X-ray photoelectron spectrum showing complete reduction of surface Cu oxide in Cu-G samples while Cu oxide is clearly present in Cu-NG samples. Plots in (d−f) have been displaced vertically for clarity.
temperature of 650 °C (Supporting Information, Figure S3). The Cu samples in our study have a majority (111) grain orientation that transforms into complete (111) grain orientation after graphene deposition (Supporting Information, Figure S4). The schematic in Figure 1b presents our experimental scheme of forming Cu-G hybrid NWs and Cu-NG NWs, to achieve fair performance comparison. First, the bare CuNW undergoes the graphene deposition process to form the Cu-G hybrid NW. Then electrical characterizations are performed to measure properties of the Cu-G NW (see Experimental Methods). Subsequently, reactive ion etching with mild oxygen plasma results in the CuNW without the graphene coating. Annealing during graphene deposition increases the Cu grain sizes24 but there is a random distribution of grain sizes (Figure 1b). Herein, we characterized a particular CuNW with and without the graphene shell to avoid sample-to-sample variations arising from varying Cu grain structures between any two distinct NWs. CuNWs were physically intact without any sign of pores or dewetting following our low-temperature rapid deposition technique (Figure 1c). We optimized the process conditions for highly selective graphene deposition on Cu, as confirmed by the presence of the characteristic Raman spectral peaks of graphene at 1350, 1600, and 2700 cm−1 on Cu-G samples and no peaks on SiO2 (Figure 1d). Complete removal of graphene in the Cu-NG samples was confirmed by the absence of graphene peaks with only the Cu fluorescence
postsynthesis transfer of graphene on CuNWs is not viable due to the lack of selectivity and uncontrolled interface properties, which makes the direct synthesis of graphene on CuNWs absolutely essential. In this work, we demonstrate selective and rapid growth of graphene on CuNWs with complete coverage. For the first time, significant enhancement of both electrical and thermal conductivity of Cu at scaled dimensions is presented by characterizing individual CuNWs first with graphene coating (Cu-G) and then after removal of graphene coating (Cu-NG). Chemical vapor deposition (CVD) is a widely used technique for graphene growth on a metal catalyst like Cu. However, achieving graphene deposition on CuNWs is challenging due to severe dewetting of thin Cu films at high temperatures needed for conventional graphene synthesis27 (Supporting Information, Figure S1). A rapid low-temperature process is critical to preserve the structural integrity of the CuNWs during graphene deposition and we present such a method in this Letter. We use plasma-enhanced chemical vapor deposition (PECVD) to conformally coat graphene on the surfaces of CuNWs at much reduced temperatures (Figure 1a). In brief, the carbon feedstock (methane) is dissociated into radicals using inductively coupled RF plasma at a fixed distance away from the sample holder (Supporting Information, Figure S2). The carrier gas (argon) transports the reactive carbon and hydrogen radicals downstream to the CuNWs, where full graphene coverage is achieved within 15 min at a deposition B
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Figure 2. Enhanced electrical conduction in Cu-G hybrid NWs. (a) Schematics illustrating partial elastic (specular) surface scattering that randomizes the momentum of few incident electrons and complete inelastic (diffuse) surface scattering that randomizes the momentum of all incident electrons along the direction of current transport. (b) Schematic illustrating grain boundary scattering of electrons at the interfaces of the grains. (c) False-colored SEM image showing the 4-probe Kelvin structure with the CuNW under test. (d) Measured resistivity values of CuNWs with (filled circles) and without graphene (open circles) coating as a function of NW width. The filled and open circles of a given color are data from a particular NW with and without graphene coating, respectively. Solid lines are resistivity values calculated from the MS−FS model for two different values of the specularity parameter p. Assuming diffuse surface scattering in Cu-NG NWs (model fit with p = 0), Cu-G NWs show partially specular scattering (p = 0.23). Grain boundary scattering contribution (black dashed line) for both Cu-G and Cu-NG NWs is identical and remains constant with width. Resistivity values for blanket Cu films (WCu ≫ TCu) with and without the graphene coating are marked on the right axis.
contact resistance from the probes. The extracted resistivity values for Cu-G and Cu-NG NWs are presented in Figure 2d along with the calculated values from eq 1. We neglect any electrical conduction in Ta and graphene layers because of their small cross sections and negligible conductivities compared to the Cu layer. In our analysis, we assume completely inelastic surface scattering (p = 0) in Cu-NG NWs due to small oxide formation (from air exposure prior to measurement) in the absence of graphene coating.13 Note that a particular CuNW with and without the graphene coating has the same internal grain-boundary structure (identical FMS) but markedly different surface scattering (different FFS). Fitting the data with these assumptions, we find that Cu-G NWs show significantly lower resistivity due to partially elastic surface scattering (p = 0.23) compared to Cu-NG NWs (p = 0). This shift toward partial elastic scattering is a direct manifestation of an oxide-free Cu surface along with the weak electronic coupling between the surface states of Cu and the low density-of-states of graphene.24 Likewise, the enhancement in elastic surface scattering is also expected for substrate-embedded CuNWs by replacing the metallic Ta coating (high density-of-states) 13,14,16 with graphene (low density-of-states). Similar enhancement of transport properties has been reported for semiconducting NWs by using a passivation layer to reduce surface recombination of carriers.30,31 To shed light on the underlying mechanism for the electrical conductivity enhancement observed in Cu-G NWs, we concentrate on the nature of electron scattering in the NWs. For a given NW after graphene deposition, the presence of graphene coating only influences the surface scattering properties. Thermal annealing during graphene deposition process causes Cu grain size expansion in the NWs. However, all measurements are performed postgraphene deposition, essentially fixing the grain boundary scattering contribution
background being detected. Furthermore, in the case of Cu-G samples, X-ray photoelectron spectroscopy scans confirmed the sp2-hybridized carbon orbitals of graphene (Figure 1e) and the complete reduction of native Cu oxide (Figure 1f). Thus, the graphene shell protects the CuNWs against oxidation upon exposure to ambient air conditions. We now compare the electrical properties of the Cu-G and Cu-NG NWs. The surface scattering (Figure 2a) and grainboundary scattering (Figure 2b) contributions to the electrical resistivity are modeled using the Fuchs-Sondheimer (FS) theory28 and the Mayadas−Shatzkes (MS) theory,29 respectively (see Experimental Methods). Using Matthiessen’s rule, the two scattering contributions can be added to get the expression for total resistivity ρ = ρbulk (FFS + FMS) ⎛1 1⎞ FFS = 2C Λ 0(1 − p)⎜ + ⎟ ⎝T W⎠ −1 ⎡ Λ0 ⎛ R ⎞ ⎛ 3α 1 ⎞⎤ ⎜ ⎟ FMS = ⎢1 − + 3α 2 − 3α 3 ln⎜1 + ⎟⎥ , where α = ⎝ ⎣ 2 dgrain ⎝ 1 − R ⎠ α ⎠⎦
(1)
Here, ρbulk = 1.72 μΩ-cm is the isotropic bulk resistivity of Cu,12 C = 1.2 is the geometric form factor for rectangular wires11 (estimated from fitting), Λ0 = 40 nm is the electron mean-free path in bulk Cu,12 p is the specularity parameter (0 for inelastic and 1 for elastic scattering), T = 60 nm is the thickness of the NW (found from AFM), W is the width of the NW and dgrain = 100 nm is the average grain size (both found from SEM), while R = 0.34 is the grain-boundary reflection coefficient.11 All parameter values are valid at 298 K. The false-colored scanning electron image in Figure 2c shows the characteristic Kelvin four-probe test structure used in this study for measuring the intrinsic CuNW resistance without the C
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Figure 3. Enhanced thermal conductivity in Cu-G hybrid NWs. (a) Resistance (R) of CuNWs as a function of square of the current amplitude (I2), varying linearly with I2. (b) Relative change in measured resistance (spheres) plotted as a function of I2 for a 180 nm wide and 10 μm long CuNW. Equation 2 was used to fit the observed values with minimized R2 fitting error (solid lines). (c) Extracted values of thermal conductivity for CuNWs of various dimensions. (d) Calculated temperature rise profile along a 10 μm long and 180 nm wide CuNW with current density J = 10 MA/cm2. Graphene-coated CuNW has significantly lower temperature in the center (hot spot) than the uncoated CuNW. (e) Calculated average temperature rise in the CuNW as a function of substrate heat loss (Qsub) for a current density J = 7 MA/cm2. Shaded region denotes the range of Qsub values lower than those observed in this work (Qsub < 0.2 Wm−1 K−1).
subsequent release, have randomized momentum in the direction of current flow. This we believe is the primary cause for complete inelastic surface scattering in our Cu-NG nanowires. On the other hand, graphene coating prevents even monolayer level oxidation of Cu-G nanowires (Figure 1f), thus creating a possibility for finite elastic surface scattering of electrons. Graphene might also affect the smooth Cu surface potential, but it was recently shown through STM and DFT studies that graphene grown at low temperatures on Cu (111) surfaces is only weakly interacting with the Cu surface states.24 The relatively weak coupling between the C 2p orbitals of
for a given NW (both with graphene and after graphene removal). The degree of elastic scattering of electrons at the Cu nanowire surfaces is highly dependent on the nature of the Cu surface potential. First-principles calculations and experiments have shown that adsorption of foreign adatoms or oxidation of the Cu surface creates perturbation of the Cu Fermi surface.13,32 In our study, Cu-NG surfaces undergo mild oxidation during the graphene removal (Figure 1f) leading to formation of defect surface states. Electrons traversing along the NW are trapped by the interface surface states and, upon D
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Figure 4. Breakdown characteristics of Cu-graphene hybrid NWs. (a) Measured relative change of resistance plotted as a function of square of the current amplitude (I2), showing the abrupt increase in resistance due to melting at high drive currents. For a given width, Cu-G NWs sustain larger drive currents before melting with the Cu-G and Cu-NG NWs having similar melting temperature. (b) Scanning electron image showing a 180 nm wide and 10 μm long Cu-G NW after breakdown. (c) Scanning electron image showing a 180 nm wide and 10 μm long Cu-NG NW after breakdown. A bigger void was observed in (b) compared to (c), possibly because of higher electron wind force (higher drive current) before breakdown in Cu-G NWs.
graphene and Cu 4p orbitals33 is believed to be responsible for the partially elastic surface scattering observed in our Cu-G wires. At this point it is imperative to provide an error estimate associated with the Cu oxidation in Cu-NG wires for the extraction of electrical conductivity. Consumption of Cu during oxide formation would reduce the conductive cross section of the NW. We estimated the extent and nature of Cu oxidation by employing a previously described technique based on the Strohmeier equation.15 High-resolution X-ray photoelectron spectroscopy scans of O 1s and Cu 2p3/2 peaks were acquired on Cu-G and Cu-NG films. O 1s scan of the Cu-NG sample has a single symmetric peak centered at 531.92 eV originating from hydroxide or hydroxyl-type oxygen (Supporting Information, Figure S7a). The Cu 2p3/2 peak scan has two distinct peaks at 934.94 eV from Cu(OH)2 and 932.76 eV from Cu (Supporting Information, Figure S7b). Therefore, we conclude that after graphene removal, Cu-NG is predominantly covered with Cu(OH)2. Although the presence of Cu2O cannot be completely neglected, it does not show up explicitly in the O 1s scan and its volume in comparison to hydroxide can be neglected in our calculations. We estimate the thickness of Cu(OH)2 layer to be 3 ± 0.5 nm (see Supporting Information S5). On the basis of the density difference of Cu(OH)2 and Cu, we conclude that 0.75 ± 0.1 nm of Cu was consumed at the three exposed surfaces of the NW. This yields only 2% error in our electrical resistivity values for the 180 nm wide Cu-NG NWs. Next, we studied the effect of improved surface scattering properties on thermal transport through the CuNWs using Joule heating experiments.34 Electric current was slowly ramped up through the CuNWs and the resultant change in electrical resistivity was continuously recorded (see Experimental Methods). Resistance increased linearly with the square of the amplitude of electric current (Figure 3a) and the rate of increase was lower for Cu-G NWs (Supporting Information, Figure S10a). To analyze the thermal transport in these NWs, we use a heat diffusion equation35 that incorporates the heat generation from Joule heating, the heat flow along the NW and the heat loss to the substrate (Supporting Information, Figure
S8). Joule heating-induced relative change in resistance can be expressed using a closed-form expression36 for on-substrate NWs R − R0 = βR (T̅ − T0) R0 ⎛ p ⎛ 2 ⎞ ⎛ mL ⎞⎞ ⎟⎟ ⎟tanh⎜ ⎜1 − ⎜ = ⎝ 2 ⎠⎠ ⎝ ⎠ Q sub − p ⎝ mL
⎛ I 2R ⎞ 0 ⎟ and m = where p = βR ⎜ ⎝ L ⎠
(2)
Q sub − p κsA
Here, T̅ is the average temperature of the NW, T0 is the temperature at the ends of the NW and the substrate temperature, βR is the temperature coefficient of resistivity for Cu, κs is the thermal conductivity of Cu, A is the cross-sectional area and L is the length of the NW, I is the electric current, R0 is the initial resistance (without Joule heating), and Qsub is the heat loss to the substrate per unit length. The resistance change is correlated to the rise in NW temperature by carefully calibrating the temperature coefficient of resistivity (βR) for individual CuNWs (Supporting Information, Figure S9). We extracted the thermal conductivity values for individual CuNWs with and without graphene coating by fitting eq 2 to the measured relative change of resistance (Figure 3b and Supporting Information, Figure S10). As the substrate heat loss Qsub is only dependent on the dimensions, thermal conductivity of the substrate, and thermal contact resistance between the substrate and the NW,37 it is assumed constant while analyzing the data for a particular NW with and without the graphene shell (see Supporting Information, S6−S8). The extracted thermal conductivities (κs) of Cu-G NWs are significantly higher (∼135−160 Wm−1 K−1) than that of CuNG NWs (∼85−105 Wm−1 K−1) for various dimensions (Figure 3c). The fitted values of Qsub for NWs of width 180 and 280 nm are 0.18 Wm−1 K−1 and 0.2 Wm−1 K−1, respectively. Note that the extracted thermal conductivities for the NWs are significantly lower than that of bulk copper (390 Wm−1 K−1). E
DOI: 10.1021/nl504889t Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters The κs reduction is a direct consequence of size scaling and has been previously observed in thin Cu films.38 The higher thermal conductivity of Cu-G NWs is consistent with the enhanced elastic surface scattering of electrons due to graphene coating. Additionally, the high thermal conductivity of graphene could provide a parallel phonon component for heat conduction.39,40 However, the thickness of graphene layer in our work (∼1 nm) is too small to have significant impact on the overall thermal conductivity of the 60 nm thick Cu-G NW. Further scaling down of CuNW thickness would surely enhance the thermal transport contribution from graphene. Higher κs but identical A and Qsub imply that a NW with graphene coating has longer thermal healing length (LH = (κsA/ Qsub)1/2)) than an uncoated NW. Longer LH indicates improved thermal conduction along the NW. Figure 3d plots the temperature rise for a given Cu-G and Cu-NG NW, and it clearly shows that Cu-G NW has lower peak temperature in the center. This is a coupled effect of lower electrical resistivity (lower Joule heating for the same drive current) and higher thermal conductivity (better heat dissipation) in Cu-G NWs. Insufficient heat dissipation from heated Cu interconnects into the surrounding dielectric is a major limiting factor in thermal management of electronic devices. Using eq 2, we estimate the temperature rise in a graphene-coated and uncoated CuNW for a range of Qsub values for a given current density (Figure 3d). The thermal benefit from graphene coating is striking for lower Qsub values with 42% lower temperature at the limit of Qsub = 0 (suspended NW). Finally, we compared the breakdown strength of Cu-G and Cu-NG NWs (Figure 4a) at extremely high drive currents. For L = 10 μm and W = 180 nm, the Cu-G NW can sustain 41% higher breakdown current than the Cu-NG NW with the same dimensions. Note that, NWs of identical dimensions break down after reaching the same relative change in resistance (ΔRBD = 75% for W = 180 nm). This is expected because ΔRBD is directly correlated with the breakdown (melting) temperature TBD. Both Cu-G and Cu-NG NWs break down at the same TBD but Cu-G NWs reach TBD at much higher drive currents. We observed greater void damage in melted Cu-G NWs compared to Cu-NG NWs (Figure 4b,c), possibly because the higher drive current in Cu-G NWs before breakdown leads to larger momentum transfer from electrons to Cu ions causing bigger voids. In summary, our work demonstrates that graphene-coated CuNWs outperform uncoated CuNWs in both electrical and thermal conductivities. Using a low temperature plasmaenhanced CVD process, we achieved uniform graphene deposition on 60 nm thick CuNWs with different widths (W = 180 and 280 nm) and lengths (L = 10 and 20 μm). Passivation of the Cu surface states with a low density-of-states material like graphene gives rise to partially elastic surface scattering and the resultant enhancement in electron transport through the NWs. Size scaling of CuNWs increases the surfaceto-volume ratio and amplifies the contribution of surface scattering over grain-boundary scattering. Therefore, Cu-G hybrids can show significant performance improvement at ultrascaled dimensions, which is highly desirable for future generations of CMOS interconnects and transparent flexible electrodes. Experimental Methods. Fabrication of Cu−Graphene Hybrid NWs. Physical vapor deposition (PVD) is used to deposit a blanket stack of 10 nm thick Ta and 60 nm thick Cu on silicon substrates with 5 μm thick thermal SiO2. CuNWs of
two different widths (180 and 280 nm) and two different lengths (10 and 20 μm) were fabricated from the thin PVD Cu films by combining e-beam lithographical patterning with argon sputter etching (see Supporting Information S3). Graphene was deposited on CuNWs at 650 °C using methane and hydrogen as the process gases and argon being the carrier gas. Remotely ignited RF plasma (550 W) provided the energy needed to break methane molecules into carbon radicals that enabled rapid graphene deposition at the significantly reduced temperature. Oxygen reactive ion etching was used to quickly remove the graphene coating from CuNWs. The plasma power (20 W) and etching time (10−12 s) were kept low enough to avoid damage to the NWs. Characterization of Cu−Graphene Hybrids. Electrical tests were performed in a Lakeshore probe station under vacuum to avoid convection losses during Joule heating experiments. Radiation losses were neglected for the small geometries considered here. The temperature of the sample chuck was controlled within accuracy of 0.1 °C for estimating the temperature coefficient of resistivity (βR) of the NWs. Raman spectroscopy measurements were carried out directly on Cu substrates with graphene at room temperature in an open-air environment using a 532 nm diode pumped solid state (DPSS) laser beam. A 50× Olympus objective (NA = 0.75, WD = 0.38 mm) was used to focus the beam on to the sample and the Raman spectra was acquired using a HORIBA LabRAM HR800 Raman spectrometer. The laser power was kept sufficiently lower than the damage threshold of graphene to avoid any heatinduced effects. For X-ray photoelectron spectroscopy measurements, photoelectrons were excited using a Mg−Kα X-ray source with energy = 1253.6 eV (SPECS XRC-1000) and analyzed using an Omicron Argus hemispherical electron analyzer with round aperture of 6.3 mm and electron takeoff angle of 45°. The resolution in binding energy of core levels was 0.2 eV. X-ray diffraction measurements were performed in a Bruker D8 focus X-ray diffractometer using the 0.15418 nm Cu Kα line. Electron Scattering in Scaled CuNWs. While traversing a metal NW, there are three major scattering mechanisms for electrons to lose momentum, namely, isotropic background scattering, surface scattering, and grain boundary scattering. Isotropic background scattering arises from phonons and point defects and constitutes the metal’s bulk resistivity (ρbulk) to electron transport. Surface scattering is typical in metal NWs of dimensions close to the electron mean-free path (Λ0), where electrons impinging the surfaces of the NWs undergo either elastic (specular) or in-elastic (diffuse) scattering depending on the perturbation of surface states (Figure 2a). The Fuchs− Sondheimer (FS) theory28 models the degree of diffuse-tospecular scattering with a specularity parameter p (p = 0 for diffuse, p = 1 for specular scattering). We use a compact form of the FS model adapted for rectangular NWs,11 as shown in the FFS term of eq 1. Grain-boundary scattering is a characteristic of polycrystalline metal wires (with short-range order) because electrons scatter while traversing across the interface between the grains (Figure 2b). The Mayadas−Shatzkes (MS) theory29 models the multiple scattering events at the grain boundaries using a reflection parameter R, as shown in the FMS term of eq 1. Values of ρbulk and Λ0 for bulk Cu were obtained from literature close to 298 K. These values are scaled using the FS and MS models to obtain effective ρ and effective Λ0 taking into account scattering at grain-boundaries and surfaces. F
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ASSOCIATED CONTENT
S Supporting Information *
Details of the plasma-enhanced chemical vapor deposition setup, fabrication process for CuNWs, XRD of Cu before and after graphene deposition, and AFM of graphene−Cu hybrid NWs. Additional details on the Cu oxide thickness estimation and thermal conductivity extraction procedure are also provided. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*(Z.C.) E-mail:
[email protected]. Author Contributions
R.M. and S.C. contributed equally to this work. Z.C. conceived and managed the project. R.M. and S.C. developed and optimized the plasma-enhanced chemical vapor deposition process. R.M. fabricated the CuNWs and performed electrical/thermal measurements. R.M., S.C., and Z.C. analyzed the data and wrote the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was sponsored by the Semiconductor Research Corporation (Task 2278.001). The authors would like to thank John Coy for technical assistance with plasma-enhanced chemical vapor deposition and Dr. Amy Marconnet for technical discussions. The authors also thank Dr. Suprem Das for help with X-ray diffraction.
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DOI: 10.1021/nl504889t Nano Lett. XXXX, XXX, XXX−XXX
