Electron Transport in Multidimensional Fuzzy Graphene

Jul 2, 2019 - Materials and methods; additional notes on XPS characterization, ... at 2 and 300 K for devices A1 and B1; and associated references (PD...
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Cite This: Nano Lett. XXXX, XXX, XXX−XXX

Electron Transport in Multidimensional Fuzzy Graphene Nanostructures Raghav Garg,† Devashish P. Gopalan,‡ Sergio C. de la Barrera,‡ Hasnain Hafiz,|| Noel T. Nuhfer,† Venkatasubramanian Viswanathan,|| Benjamin M. Hunt,*,†,‡ and Tzahi Cohen-Karni*,†,§ †

Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States || Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States § Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States

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‡

S Supporting Information *

ABSTRACT: Atomically thin two-dimensional (2D) materials offer a range of superlative electronic and electrochemical properties that facilitate applications in sensing, energy conversion, and storage. Graphene, a 2D allotrope of carbon, has exceptional surface area per unit mass and highly catalytic edges. To leverage these properties, efforts have been made to synthesize complex three-dimensional (3D) geometries of graphene, with an eye toward integration into functional electronic devices. However, the electronic transport properties of such complex 3D structures are not well understood at a microscopic level. Here, we report electron transport in a 3D arrangement of free-standing 2D graphene flakes along an isolated one-dimensional Si nanowire. We show that transport through the free-standing graphene network is dominated by variable-range hopping and leads to negative magnetoresistance, from cryogenic conditions up to room temperature. Our findings lay the foundation for studying transport mechanisms in 2D material-based multidimensional nanostructures. KEYWORDS: 3D Graphene nanostructures, variable-range hopping, electron transport, magnetoresistance

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standing on the surface of a one-dimensional (1D) intrinsic silicon nanowire (i-SiNW) as illustrated in Figure 1a. The isolated nanowires were used to fabricate mesoscopic devices for magneto-transport measurements. Using a well-controlled synthesis protocol, we precisely tailor the density of exposed graphene planes and edges along each iSiNW by controlling the synthesis temperature of graphene flakes (Figure 1b and c; see Supporting Information for detailed synthesis protocol). Through this, we control the arrangement of free-standing graphene flakes, exposing both surfaces of each flake to maximize the overall surface area and number of exposed edges. Increasing the synthesis temperature from 700 (condition A) to 1100 °C (condition B) increases the graphene flake size and density, observed through the increase in NT-3DFG diameter from 120 ± 20 to 250 ± 20 nm, respectively (Figures 1b and c and S1). We attribute the increase in graphene flake size to the enhanced nucleation and growth rates as synthesis temperature is increased.16,17 The polycrystalline network of flakes is mostly composed of a sp2 carbon lattice with edge exposing single- to few-layer free-standing graphene (for

raphene’s exceptional surface area per unit mass (theoretically up to 2630 m2 g−1)1 and catalytically active edges2,3 have spurred immense interest in creating threedimensional (3D) nanostructures for applications in sensing,4 energy conversion, and storage.5 Efforts to synthesize graphenebased 3D nanostructures have resulted in polycrystalline graphene flakes arranged in complex networks.6−8 Electrontransport mechanisms in two-dimensional (2D) single-crystal graphene films have been extensively studied with regard to the material’s structure (e.g., edge termination,9,10 defect type and density,11 crystallinity,12−14 flake orientation, and layer stacking15). However, the underlying mechanisms cannot be directly extrapolated to polycrystalline 3D nanostructures because of the added dimensionality and intricate morphology. Thus, integrating a 3D arrangement of graphene flakes into functional electronic devices and developing a fundamental understanding of electron transport in such structures at a microscopic level remains an open challenge. In this work, we synthesize a multidimensional graphenebased nanostructure: nanowire templated-3D fuzzy graphene (NT-3DFG) and investigate the electron transport mechanisms in this novel 3D geometry of free-standing graphene. We recently reported the synthesis of NT-3DFG meshes.8 Here, we isolate single NT-3DFG nanowires, each of which is composed of highly controlled 3D arrangement of graphene flakes free© XXXX American Chemical Society

Received: May 1, 2019 Revised: June 23, 2019 Published: July 2, 2019 A

DOI: 10.1021/acs.nanolett.9b01790 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. Morphology of NT-3DFG. (a) Schematic representing NT-3DFG composed of free-standing 3DFG flakes on a SiNW core. Representative HRTEM image of NT-3DFG synthesized under (b) condition A and (c) condition B. Scale bars are 100 nm. Black and white arrows denote single and multilayer graphene flakes, respectively. Expanded view of marked red dashed area is available in Figure S4.

Figure 2. Structural composition of NT-3DFG. (a) Representative (I) STEM image (scale bar is 50 nm), (II) schematic representing the cross-section of NT-3DFG, and (III) corresponding EELS acquired from points (empty circles marked in panel I), along the radius of NT-3DFG synthesized under condition A. (b) Representative (I) STEM image (scale bar is 100 nm), (II) schematic representing the cross-section of NT-3DFG, and (III) corresponding EELS acquired from points (empty circles marked in panel I) along the radius of NT-3DFG synthesized under condition B. Red and blue lines denote graphene and graphite-like EELS spectra, respectively. Gray region denotes extended fine structure in EELS spectra.

all the simulations also show transitions from 1s to π* states at ∼285 eV and 1s to σ* states at 292.2 eV (Figure S5a). The extended fine structure of the EELS spectra shows oscillations originating from the multiple scattering interferences.21 The intensity of the interference peaks depends on the number of neighboring atoms (in- and/or out-of-plan) surrounding any absorbing atom.21 Therefore, the intensity of the interference peaks is a good indicator to distinguish between graphene-like and graphitic structures. From the extended fine structure of the simulated EELS spectra, we identified two signature peaks located at ∼311 and ∼325 eV, respectively (black arrows, Figure S5a). The intensity of both peaks increases with increasing number of graphene layers, although the intensity of the peak at ∼325 eV is stronger than that at ∼311 eV (Figure S5b). In our experimental EELS spectra, the interference peaks are observed as prominent convoluted features at ∼320 eV (gray regions of position 8 in Figure 2a.III and position 6−8 in Figure

additional information on XPS, Raman spectroscopy, and TEM characterization, see Supporting Information). In NT-3DFG, free-standing graphene flakes form a dense structure surrounding the i-SiNW core, Figure 2a.I and b.I. Schematics illustrating the internal structure of NT-3DFG, across a longitudinal cross-section, are presented in Figure 2a.II and b.II for conditions A and B, respectively. Analysis of the carbon K-edge region in electron energy loss spectra (EELS) acquired from multiple points across the radii of NT-3DFG reveals a sharp peak at 285.5 eV due to the transition from 1s to π* states and a broad peak between 290 and 310 eV due to the transition from 1s to σ* states (Figure 2a.III and b.III).18,19 The emergence of such transitions confirms sp2 lattice of graphene.20 To identify the constituent structures in NT-3DFG, we performed theoretical EELS spectra simulations (Figure S5; see Supporting Information for detailed EELS simulation protocol). The energy-loss near-edge fine structure (ELNES) spectra from B

DOI: 10.1021/acs.nanolett.9b01790 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 3. Electron transport in single NT-3DFG. (a) Optical image of a representative single NT-3DFG device (scale bar is 5 μm). Resistance as a function of temperature acquired from single NT-3DFG devices (b) A1 and (c) B1. Empty circles and solid black lines denote experimental data and parallel resistance electron transport model fit, respectively. Insets present VRH component of the measured four-terminal resistance (empty circles) and theoretical VRH resistance determined from the parallel resistance model (black solid line) as a function of T−0.25 (gray regions denote deviation from proposed model at low temperatures). (d) Schematic representing the cross section of NT-3DFG highlighting the origin of R0 and RVRH, respectively.

Figure 4. Magnetoresistance of single NT-3DFG. Magnetoresistance as a function of applied perpendicular magnetic field acquired from single NT3DFG devices (a) A1 and (b) B1. (c) Magnetoresistance at 9 T as a function of device temperature. Data is presented as mean ± standard deviation (n = 3).

2b.III). In the case of condition A, the majority of the radial structure is composed of free-standing single-layer graphene (positions 1−7, Figure 2a.I and a.III), as indicated by extended fine-structure EELS analysis (Figure 2a.III).18,22,23 While, in the case of condition B, a thicker graphitic shell (positions 6−8, Figure 2b.I and b.III) underneath single-to-few layer freestanding graphene flakes is observed (positions 1−5, Figure 2b.I and b.III). Thus, synthesis under condition B leads to a higher density of free-standing graphene flakes, as well as a thicker graphitic shell, compared to that under condition A. To probe the electronic transport of NT-3DFG, we performed low-temperature four-terminal magneto-transport measurements on single NT-3DFG devices (Figures 3a and S6a; see Supporting Information for detailed device preparation and measurement protocols). We measured 3 devices each for conditions A (devices A1, A2, and A3) and B (devices B1, B2, and B3). All devices within a synthesis condition exhibited qualitatively identical behavior (Figures S7 and S8 and Table S6); here, we focus our attention on devices A1 and B1 for conditions A and B, respectively (additional devices are presented in the Supporting Information). We observe that the resistance of single NT-3DFG devices increases monotonically with decreasing device temperature (Figure 3b and c). The resistance increases by a factor of 4.7 (Figure 3b; 0.25 MΩ at 300 K to 1.17 MΩ at 2 K) and 1.4 (Figure 3c; 18.14 kΩ at 300 K to

26.13 kΩ at 2 K) for devices A1 and B1, respectively. We note that electron transport in NT-3DFG occurs only through templated fuzzy graphene; no conduction was observed in iSiNW devices. We find that the net resistance of NT-3DFG, R(T), can be deconvolved into individual resistance components: R0, a temperature-independent resistance, and RVRH, a temperaturedependent resistance. Because of the presence of both freestanding graphene flakes and a graphitic shell in templated fuzzy graphene, we employ a parallel resistor model to describe the temperature-dependent transport. A schematic illustrating this electron conduction mechanism is presented in Figure 3d. Electron transport in graphite exhibits metallic behavior because of the overlap between the valence and conduction bands.24 Graphite’s electrical resistivity is weakly dependent on temperature,25−27 whereas our devices show a much stronger temperature dependence. Therefore, we approximate the resistance contribution from the graphitic shell (R0) as being temperature independent. The free-standing flakes in templated fuzzy graphene are in contact with each other along defect-rich edges. Transport in similar disordered graphene structures has been described by variable-range hopping (VRH) through localized states.28−30 The temperature dependence of VRH leads to a resistance given by C

DOI: 10.1021/acs.nanolett.9b01790 Nano Lett. XXXX, XXX, XXX−XXX

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stronger the negative MR.33 Hence, the observed negative MR becomes stronger upon cooling (Figure 4.c). In condition A devices, the resistance is dominated by the VRH mechanism since R0 is much greater than RVRH over the majority of the measured temperature range (Table S8, RVRH(2 K) = 5.05 MΩ, RVRH(300 K) = 30.16 kΩ, and R0 = 1.71 MΩ for device A1). The combined negative MR at 9 T and 300 K from the VRH component is ∼1%. As the temperature is lowered, RVRH(T) increases, increasing the magnitude of negative MR up to ∼3%. However, at the lowest temperatures, RVRH increases to ∼5 MΩ, larger than the resistance of the graphitic channel R0. Thus, the MR effect is obscured by the lower resistance path through the graphitic shell. Therefore, there is an intermediate temperature, T*, for which the negative MR effect is the strongest in the condition A devices, as observed near 20 K in Figure 4.c. From the total measured MR at 2 K and 9 T for device A1, the VRH component of resistance is estimated to be RVRH(9 T) ≈ 3.3 MΩ. Although shunting through the graphitic shell reduces the magnitude of the measured MR, the MR resulting from pure VRH is expected to be significantly larger, (MR(9 T) ≈ ((3.3 MΩ − 5 MΩ))/5 MΩ = −34%). For optimal synthesis conditions, it may be possible to reduce the formation of the graphitic shell, enabling magnetic-field-sensing applications with NT-3DFG dominated by VRH. In conclusion, atomic and macroscopic scale structural characterization allow us to establish an understanding of the electron transport mechanisms in graphene-based complex 3D nanostructures. We demonstrate highly controlled synthesis of NT-3DFG, a polycrystalline 3D arrangement of 2D graphene flakes along a 1D SiNW. Using templated fuzzy graphene as a model, we establish the underlying electron transport mechanisms in multidimensional graphene nanostructures. Electron transport in templated fuzzy graphene occurs through parallel channels formed by the graphitic shell (metallic transport) and the free-standing graphene (VRH-based transport). In addition, the material exhibits negative MR at all temperatures, regardless of flake size and density, which we attribute to a VRH-based interference mechanism distinct from weak localization. While the observed MR magnitudes are on the order of −1% to −4%, parallel transport through the graphitic shell suppresses potentially large negative MR behavior in the free-standing graphene flakes. Our study opens new avenues for synthesizing and characterizing 3D arrangement of 2D materials to understand electron transport in multidimensional nanostructures.

(1)

where R1, T0, and d are a constant of proportionality, the Mott characteristic temperature, and the dimensionality of hopping, respectively.31 We apply the VRH model along with a parallel resistance to describe the measured four-terminal resistance in NT-3DFG, leading to R(T ) = R 0R VRH/(R 0 + R VRH)

(2)

where R0 is a temperature-independent resistance from the graphitic shell and RVRH is described by eq 1. On the basis of standard regression analysis, we find that 3D VRH (d = 3) best describes the temperature-dependent transport in all NT-3DFG devices measured, although the quality of fit does not strongly depend on dimensionality (Figures 3b, c and S7). The trend of increasing resistance with decreasing temperatures and successful fits using eq 1 suggests the presence of 3D hopping in the network of free-standing graphene flakes. The extracted values for R0 for devices A1 and B1 were 1.71 MΩ and 26.13 kΩ (Table S6), respectively. These values agree with previously reported resistivity magnitudes for graphitic structures (Table S7). The difference in R0 magnitude between conditions A and B is consistent with the EELS analysis, corroborating a sparser graphitic shell around the i-SiNW in condition A as compared to that in condition B. Additionally, the VRH component of the measured resistance fits well with the theoretical model down to ∼7 K, below which other effects such as Coulomb interactions32 cause deviation from the model defined by eq 2 (insets, Figure 3b and c). In the presence of magnetic fields up to ±9 T, perpendicular to the length of the nanowire, NT-3DFG exhibits negative magnetoresistance (MR) at all temperatures between 2 and 300 K (Figure 4a and b). We attribute the observed negative MR to a VRH-based mechanism in the free-standing graphene flakes. VRH-based electron transport in the presence of a magnetic field can result in an anomalously large negative MR because of an orbital quantum interference effect, as first described by Ioffe and Spivak.33 Physically, a long-distance hop comprises multiple parallel paths, each with intermediate scattering sites. In the absence of a magnetic field, these multiple paths interfere destructively, providing an extra contribution to the resistance. Introducing a perpendicular magnetic field suppresses this destructive interference, resulting in a negative MR.33,34 We note that this effect is physically distinct from often-cited mechanism of weak localization,35 which is typically only relevant at low temperatures and low magnetic fields compared to what we observe in NT-3DFG devices.36,37 Although the predicted magnitude of negative MR associated with VRH can be quite large (up to ∼70%),33 the observed MR is relatively weaker in our devices due to parallel conduction through the graphitic shell. Furthermore, we find that there is a distinction in the temperature dependence of the MR between the two synthesis conditions (Figure 4c). While condition B devices show a progressively stronger negative MR at lower temperatures, condition A devices show a maximum magnitude of negative MR at ∼20 K, below which the MR was observed to become weaker. To understand this behavior, we consider the monotonic case first. As condition B devices are cooled down, the VRH resistance component becomes extremely insulating relative to the resistance of the graphitic shell (Table S8; RVRH(2 K) = 1.66 MΩ, RVRH(300 K) = 61.59 kΩ, and R0 = 26.13 kΩ for device B1): the more insulating the VRH component, the

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.9b01790. Materials and methods; additional notes on XPS characterization, Raman characterization, HR-TEM of NT-3DFG; figures showing SEM characterization, XPS characterization, Raman characterization, HRTEM and SAED characterization of NT-3DFG, simulation of EELS spectra, isolated NT-3DFG device schematic and characterization, and electrical and magnetoresistance characterization of devices A2, A3, B2, and B3; tables showing the data summary of Raman analysis of isolated NT-3DFG, data summary of dual laser Raman analysis of isolated NT-3DFG, summary of interplanar spacing D

DOI: 10.1021/acs.nanolett.9b01790 Nano Lett. XXXX, XXX, XXX−XXX

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determined from SAED, data summary of electron transport model fitting parameters for all devices, data summary of graphitic shell resistivity for all devices, and data summary of R0 and RVRH at 2 and 300 K for devices A1 and B1; and associated references (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Raghav Garg: 0000-0002-3501-6892 Venkatasubramanian Viswanathan: 0000-0003-1060-5495 Tzahi Cohen-Karni: 0000-0001-5742-1007 Author Contributions

R.G. performed material synthesis, SEM, Raman, and XPS characterization. R.G. and N.T.N performed HRTEM, STEM, and EELS. H.H. performed EELS simulations under the supervision of V.V. R.G., D.P.G, and S.C.d.l.B performed device fabrication and magneto-transport measurements. B.M.H. and T.C.-K. supervised the research. All authors discussed the research and the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS T.C.-K. would like to thank the National Science Foundation (CBET-1552833) and the Office of Naval Research (N000141712368). B.M.H. was supported by the Department of Energy under the Early Career award program (DESC0018115). D.P.G. and S.C.d.l.B. were supported by the Department of Energy (DE-SC0018115) for fabrication of the nanodevices and the magneto-transport measurements. H.H. acknowledges support from the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy under the Fuel Cell Technologies Office (DE-EE0008076). V.V. acknowledges support from National Science Foundation (CBET1554273). We thank Carnegie Mellon University Nanofabrication Facility and the Department of Materials Science and Engineering Materials Characterization Facility (MCF677785). We also thank M. V. S. Chandrashekhar and David Pekker for their assistance with modelling electron transport.

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DOI: 10.1021/acs.nanolett.9b01790 Nano Lett. XXXX, XXX, XXX−XXX