Effect of grain boundaries on charge transport in CVD-grown bilayer graphene

Accepted Manuscript Effect of grain boundaries on charge transport in CVD-grown bilayer graphene Jun Wu, Yongchao Li, Danfeng Pan, Chenghuan Jiang, Chen Jin, Fengqi Song, Guanghou Wang, Jianguo Wan PII:

S0008-6223(19)30252-0

DOI:

https://doi.org/10.1016/j.carbon.2019.03.029

Reference:

CARBON 14034

To appear in:

Carbon

Received Date: 15 November 2018 Revised Date:

26 February 2019

Accepted Date: 11 March 2019

Please cite this article as: J. Wu, Y. Li, D. Pan, C. Jiang, C. Jin, F. Song, G. Wang, J. Wan, Effect of grain boundaries on charge transport in CVD-grown bilayer graphene, Carbon (2019), doi: https:// doi.org/10.1016/j.carbon.2019.03.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Graphical abstract

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The pronounced metallic character of grain boundary is observed in bilayer graphene

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bicrystals synthesized using the solid-state-source CVD method, which is dramatically different from individual grains. Electrical transport measurements show that individual boundaries between coalesced grains impede electrical transport,

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suppress the magnetoresistance and enhance intervalley scattering in graphene.

ACCEPTED MANUSCRIPT Effect of grain boundaries on charge transport in CVD-grown bilayer graphene

Jun Wu

a, b

, Yongchao Li a, Danfeng Pan c, Chenghuan Jiang

a, b

, Chen Jin d, Fengqi Song

a, e

,

a

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Guanghou Wang a, e, and Jianguo Wan a, e,∗

National Laboratory of Solid State Microstructures, Department of Physics, Nanjing University,

Nanjing 210093, China

Institute of Applied Physics, Department of Mathematics and Physics, Nanjing Institute of

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b

Technology, Nanjing 211167, China

School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China

d

College of Engineering and Applied Sciences, Nanjing University, Nanjing 210093, China

e

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c

Collaborative Innovation Center for Advanced Microstructures, Nanjing University, Nanjing

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210093, China

∗

Corresponding author. Collaborative Innovation Center for Advanced Microstructures, Nanjing University,

Nanjing 210093, China. E-mail address: [email protected] (J. Wan). 1

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Abstract:: Grain boundaries (GBs) in polycrystalline graphene could significantly modulate the

physicochemical properties of graphene films, and have attracted intense interest. However, fundamental magnetotransport mechanisms of GBs in bilayer graphene grown by chemical vapour deposition (CVD) are scarcely reported. In this work, we synthesize bilayer graphene bicrystals on

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polycrystalline Cu foils and measure the electronic properties of such grains as well as of individual graphene grain boundaries. Interestingly, the pronounced metallic character of GB is observed, which is dramatically different from individual grains. Large linear magnetoresistance in graphene

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bicrystals is observed, which attributes to inhomogeneous charge transport, decorated by quantum interference effects at low temperatures. The measurement data show that individual boundaries

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between coalesced grains impede electrical transport, suppress the magnetoresistance and enhance intervalley scattering, leading to degradation of electrical performance of CVD graphene. Nevertheless, GBs embedded in a perfect graphene sheet can tune its electronic structure at the nanoscale, act as quasi-one-dimensional metallic wires and can be used as good candidates for

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strong magnetic field sensors. This work is beneficial to the fundamental understanding of the role of GBs in CVD-grown graphene and opens a potential avenue of application for polycrystalline bilayer graphene in functional devices.

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deposition

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Keywords: grain boundary, magnetoresistance, weak localization, bilayer graphene, chemical vapour

2

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1. Introduction

Graphene has attracted intense attention worldwide due to its fascinating physical properties, such as superior mechanical strength and stiffness [1], electronic and thermal conductivity [2,3], transparency [4], and its potential applications for straightforward incorporation into current silicon

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and plastic technologies [5,6]. CVD (chemical vapour deposition) method is economically and technically more feasible approach to synthesize high-quality monolayer/bilayer graphene at wafer

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scale [7]. Unfortunately, CVD-grown graphene is intrinsically polycrystalline, with pristine graphene grains stitched together by disordered grain boundaries (GBs) which are extended defects

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made up of non-hexagonal rings [8,9]. GBs break the lattice symmetry and are believed to have a great impact on electronic structure and transport properties of polycrystalline graphene [10-12]. Beyond that, these topological line-defects exhibit an increased chemical reactivity, suggesting their potential application to sensing or as templates for synthesis of one-dimensional materials [13,14].

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Despite the important roles played by GBs in the electronic transport of polycrystalline CVD graphene, relatively small numbers of works have been devoted to the experimental examination of

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the microscopic effects of an individual boundary.

Recently, semiconducting bilayer graphene became a subject of intense research due to the

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low-energy Hamiltonian of chiral quasiparticles and a Berry phase of 2π. Besides the electrical bandgap opening by vertical electric fields, the observed non-saturating linear behavior of magnetoresistance (MR) in bilayer graphene has attracted considerable attention, which is obscured by the co-occurrence and interplay of doping, mobility fluctuations and a polycrystalline structure. The quantum model (Abrikosov) [15,16] was used to interpret linear MR in multilayer epitaxial graphene [17,18], while the classical model (Parish and Littlewood, PL) [19,20] was argued that the

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ACCEPTED MANUSCRIPT behavior was governed by “built-in mosaic tiling” in epitaxial bilayer graphene [21]. Two-fluid model [22] was recently employed in compensated graphene bilayer taking into account electron-hole recombination and finite-size sample geometry [23]. Therefore, a deeper understanding of the physics behind the linear MR is of great importance. The effect of weak

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(anti)localization WL (WAL), is a sensitive tool of quantum interference for studying quantum system. In single-layer graphene a Berry phase of π creates WAL, while the effect disappears in

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bilayers, which have a Berry phase of 2π. Unlike in single-layer graphene, suppression of elastic backscattering is not expected, and the quantum correction to the conductivity in a bilayer will have

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the sign of conventional WL. However, its magnitude as a zero-field peak in magnetoresistance will still be very sensitive to the details of elastic scattering processes [24]. In the previous works, GBs were known as the main culprits that impede electrical transport, and induce prominent weak localization indicative of intervalley scattering in graphene [25,26].

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However, other studies show that electrical performance of the graphene device is not significantly degraded by the GBs in case of well-stitched CVD graphene [11,27]. The debate over effect of GBs

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on charge transport can help us to comprehend the structure and properties of graphene GBs. This is especially useful for understanding and controlling of the transport properties of macroscopic CVD

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graphene, which is indispensable for the prospective device application. In this study, we aim at bilayer graphene bicrystals synthesized using the solid-state-source CVD method, and show how individual boundaries between coalescing grains affect graphene’s electronic properties. Spatial Raman mapping was carried out and reveals that GBs scatter charge carriers. Electrical transport properties in bilayer graphene are experimentally investigated by varying magnetic-field strength and the temperature. We found out that the boundary (i) enhances the resistance with the increment 4

ACCEPTED MANUSCRIPT growing roughly linearly with the temperature, (ii) suppresses the large positive linear magnetoresistance, and (iii) enhances the intervalley scattering rate. This study highlights the importance of grain interfaces, especially on the carrier transport properties in CVD graphene. 2. Experimental Section

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Graphene Synthesis and Characterization: The graphene grains were synthesized on copper foils (25 mm thick, 99.8% purity, Alfa Aesar, product no. 46365) by the CVD process at ambient pressure [28]. Solid polystyrene powder was performed as the carbon precursor. The grown

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graphene bicrystals with distinguishable GB were transferred onto highly doped Si substrates topped with 300 nm SiO2, using the poly(methylmethacrylate) (PMMA)-assisted technique. The

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morphology and microstructure of samples were characterized by optical microscopy (OM) and scanning electron microscopy (SEM) with a Sirin 200 SEM at 5 kV. Atomic force microscopy (AFM) images were obtained with a scanning probe microscope (NT-MDT Co.). Raman spectroscopy and spatial Raman mapping were performed on an NTEGRA Spectra Nanolaboratory

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(NT-MDT Co.). The laser excitation wavelength was 633 nm and the intensity of Raman peak was extracted from the maximum value after baseline subtraction over corresponding spectral range (1295–1365 cm−1 for D peak, 1540–1650 cm−1 for G peak and 2560–2750 cm−1 for 2D peak).

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Device Fabrication and Measurements: Two-step standard photolithography processes were performed to pattern the graphene grains and deposit electrodes. In one lithography step, followed

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by O2 plasma etching by the inductively coupled plasma process, excess of graphene flakes was etched away to remove the electrical pathways between electrodes through undesired graphene flakes. In another step, electrode patterns were transferred onto the sample and Cr/Au (5/40 nm thick) as contact metals were deposited by electron beam evaporation. The samples were thermally annealed in a H2/Ar atmosphere at 400 °C for 1 hour to remove the residues from the fabrication process. The electrical performance of the devices was further improved by current annealing at liquid helium temperatures and in vacuum. Four-terminal electrical measurements were used for 5

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transport characterization. For current annealing process, the applied dc current across the flake was ramped up with a sweeping rate of ~5µA/s up to a predefined set-point, which was monitored with a Keithley 2400 voltage source meter. The maximum current flowing through the device normalized to the graphene width does not exceed 2mA/µm. Electronic transport measurements discussed below

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were carried out by the standard lock-in technique, using Quantum Design PPMS with a fixed excitation current of 20 µA. The temperature during measurements ranged from 2 K to 298 K, and a magnetic field up to 9 T was applied.

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3. Results and Discussion 3.1. Characterization of Graphene GBs

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The bilayer graphene grains used in this study are synthesized using the solid-state-source CVD method by the synchronous growth mechanism, which makes both the upper and lower layers grow simultaneously at almost the same rate (see details in experimental section). In the synchronous growth mode, bilayer graphene domain edges propagate laterally on the Cu surface and merge, resulting in the interface lines, which act as scattering lines and will be shown below.

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The morphology of the grains on Cu foils is visualized in Fig. S1(a) using a simple thermal annealing process (see Supporting Information) [29]. Figs. S1(b) and S1(c) show typical optical

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images and scanning electron microscope (SEM) photograph of graphene domains transferred onto the SiO2/Si substrate, respectively. These domains consist of either a single grain or a few coalesced

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grains. Each grain was typically hexagonally shaped, with ~120° corners, suggesting that their edges are approximately aligned with the zig-zag directions, which is confirmed by the Raman spectrum having a very low intensity of D bands even at the grain edges (Fig. 1(a)) [25,30]. It should be noted that this synchronous growth mechanism is very different from the common layer-by-layer growth process. Raman mapping was collected from as-grown bilayer graphene domains (Fig. 1(a)–(e)), which is an effective method to determine the layer number of graphene and the presence of defects in graphene. All these spectra show that the ratio of 2D to G peak intensity is in the range of 0.8–1.1, 6

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the FWHM of 2D bands is mostly in the range of 38–46 cm−1, and the position of 2D peaks locates at 2650–2656 cm−1, suggesting that the graphene crystallite is bilayer. Additionally, 2D peak shown in Fig. S2 can be deconvoluted into four peaks, corresponding to the four permissible photon transition processes in characteristic bilayer graphene. The disorder-induced D bands (~1335 cm−1)

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obtained in the merging region of the grains provide a strong evidence for the defective nature of the GB region (Fig. 1(a)). The GBs have the D to G peak intensity ratios ~0.1. Therefore, single-crystalline hexagonal graphene grains grow discretely and subsequently coalesce together

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forming an individual GB. Raman mapping of the D peak intensity provides a particularly convenient way to clearly identify the locations of grain boundaries. Fig. 1(f) shows typical Raman

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spectra recorded at different points of graphene domains and GBs. Raman D peak indicates an

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intervalley scattering process, which involves the presence of sharp defects in GB [25].

Fig. 1 Spectroscopic Raman mapping of graphene grains and grain boundaries on a SiO2/Si substrate. (a) D peak intensity, (b) G peak intensity, (c) 2D peak intensity, (d) FWHM of the 2D 7

ACCEPTED MANUSCRIPT band, and (e) position of the 2D peak maps of polycrystalline bilayer graphene flakes. (f) Representative Raman spectra taken from the locations inside a single-crystal graphene grain and on the grain boundary between two coalesced graphene grains. Scale bar in panels (a)–(e) is 5 µm. 3.2. Electrical transport measurements

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We have performed electrical transport measurements on graphene bicrystals because the GB is easily identified and located. Fig. 2(a) shows a typical device with multi-terminal electrodes on graphene bicrystal that allow simultaneous measurements of both intra-grain (within grain) and

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inter-grain (across GB) electrical properties. For four-terminal measurements, two outer electrodes were used as the source (S) and drain (D) electrodes. Fig. 2(b) shows representative output

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characteristics for both intra-grain and inter-grain measured at room temperature for this device. All the current–voltage curves are linear. The resistances extracted from the slopes of these curves are RL ~810 Ω (electrodes 1–2), RR ~790 Ω (electrodes 3–4) and RCG ~2040 Ω (electrodes 2–3), respectively. The inter-grain resistivity, normalized to the graphene geometry, ρCG ~4173 Ω/□ is

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higher than both of the intra-grain resistivities (ρL ~3097 Ω/□ for the left grain and ρR ~3216 Ω/□ for the right grain). If we ignore the effect of GB, an inter-grain series resistance (R* ~1553Ω) can be calculated by simply integrating the intra-grain resistivities. Accordingly, a GB resistance (RGB =

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RCG - R*) of 487 Ω is yielded (or ρGB ~5.8 KΩ·µm when scaled by the graphene GB length), using

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an equivalent resistance model [10,31]. This “extra” resistance in the GB region reflects the effect of enhanced scattering at GB defect sites. In order to analyze the temperature (T) dependent change of resistivity, we define the relative change in resistivity normalized by room temperature value as ρ(T)/ρ(298 K). In Fig. 2(c), the resistivity exhibits two distinct behaviors between intra-grain and inter-grain. An appreciable monotonic reduction of ρ(T)/ρ(298 K) is observed with decreasing T, suggesting that the inter-grain exhibits a metallic character which can be mostly ascribed to electron–phonon scattering [32,33]. The observation of metallic behavior of GB supports recent scanning tunneling microscopy and 8

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spectroscopy measurements [34,35]. We also note that there are slight upturns in ρ(T)/ρ(298 K) at the low temperature range (T < 7.4 K) due to the enhanced effect of electron–electron interaction [36] and the onset of weak localization observed in the next magnetotransport measurements. On the other hand, a small resistivity change of less than 5% is observed in the wide temperature range

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2–298 K, indicative of a nonmetallic T dependence of the intra-grain region. This suppressed temperature dependence further suggests that the dominant scattering mechanism likely stems from static impurities [32,33,37]. Interestingly, a linearly increasing ρ(T) of inter-grain is observed,

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indicative of electron–phonon interaction as the dominant source of carrier scattering. This is consistent with the Boltzmann model [38,39]. The change of resistivity is linear T dependent for

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sufficiently high temperature T > TBG (the Bloch-Grüneisen temperature TBG = 2ℏυphkF/kB ~110 K in Fig. 2(c)), written as ∆ =

ℏ

,

(1)

where d is the deformation potential, kB is the Boltzmann constant, ρm is the graphene mass density,

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υph = 2×104 m/s is the longitudinal acoustic phonon velocity [40,41] and υF = ℏkF/m* ~0.9×106 m/s is the Fermi velocity (kF and m* are the Fermi wave vector and the effective mass in bilayer graphene, respectively.). Equation (1) determined slope gives d ~108 eV, much larger than the value

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in graphite and exfoliated graphene [33,38,39]. Such a high deformation potential is attributable to enhanced phonon scattering at structure-disordered GB. The difference of T-dependent resistivity in

of GBs.

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intra-grain and inter-grain shows that there are abundant physical effects in the electrical transport

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ACCEPTED MANUSCRIPT Fig. 2 (a) Optical image of the multi-terminal device on two merged graphene grains (indicated by dashed lines). (b) Representative room-temperature I–V curves measured within each graphene grain and across the grain boundary. (c) The relative change of resistivity normalized for room temperature value as a function of temperature.

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Magneto-transport properties of the specimens were investigated in a magnetic field with direction perpendicular to the sample plane. The MR was estimated by the following relation: MR % =

− 1 × 100%,

(2)

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where R(B)and R(0) are the resistance with and without the magnetic field B, respectively. MR data

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of the intra-grain and inter-grain measured at 3.2 K are shown in Fig. 3(a). The curve changes from a cusp to a linearly rising behavior with the increase of magnetic field without sign of saturation. Strikingly, we observed a linear MR of intra-grain with its value 78% at 3.2 K and 5 T, and the field sensitivity of MR was established to exceed 15%/T. The other intra-grain region also exhibits equally large magnetoresistance. The plots of MR data against external magnetic field show MR

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can be linearly fitted well by B above a threshold field, as shown in Fig. 3(b). However, the corresponding MR of inter-grain only reaches a maximum of 19%, indicating that the GB has an

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inhibitory effect on magnetoresistance. Similar results were obtained for the other samples. Figs. 3(c) and 3(d) give an overview of the magnetic field dependence of MR at a series of temperatures.

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Especially for inter-grain region, the linear MR does not saturate with magnetic fields up to 9 T and is essentially temperature independent. This means that graphene GBs can be used as good candidates

for

strong

magnetic

field

sensors,

opening

the

way

towards

designing

magneto-electronic devices based on graphene GBs. Shubnikov-deHaas oscillations (SdHO) were observed at low temperatures in Figs. 3(c) and 3(d), indicating that large linear MR does not meet Abrikosov’s quantum model, which demands all of the carriers coalesce into the lowest Landau level. The SdHO originate from the successive emptying of Landau levels with an increasing magnetic field. Thus the system is not in the quantum limit while the SdHO are observed. 10

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Furthermore, it is well known that the conditions for the quantum linear MR are ℏωc ≫ kBT and n ≪ (eB/ℏ)3/2, where n is carrier density. In the present study, the p-type carrier density n ≥ 1.1×1012 cm−2 in our samples was obtained from the field-effect method [28], and the equivalent condition for the two-dimensional system, n ≪ eB/ℏ, should be used instead. For monolayer/bilayer graphene,

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it can easily meet the criterion ℏωc ≫ kBT at low temperature [42-44]. Considering the four-fold (spin and valley) degeneracy of the bilayer graphene, the Landau level fillings should be less than 4 for the system to be in the quantum limit. Therefore, the magnetic field should be larger than n(ℏ/4e)

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= 11.4 T to fulfil the quantum limit condition, which is higher than the value presented in our experiment. Consequently, quantum MR model is excluded. We suggest that the observed positive

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linear MR may be attributed to PL’s classical model [45,46]. The core of this model is that the inhomogeneities produce the large spatial fluctuations in the conductor tensor and induce the linear MR. It is worth noting, however, the magnetoresistance observed in the present study is much larger than that in epitaxial bilayer graphene, possibly resulting from the difference in the origin of the

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mosaic tiling [21]. For the latter, segmentation of the electronic structure due to partial dislocations (interface lines between AB and AC stacked regions in epitaxial bilayer graphene) is the only ingredient that leads to classical linear MR. By contrast, defects, ripples, boundaries and local

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contaminant may be produced in CVD graphene during the fabrication process, which result in a nonuniform charge/mobility spatial distribution and are responsible for electro/magneto transport

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properties (Figs. S3(a) and S3(b) in the Supporting Information) [47-49]. Note that a not-strict linear dependence of intra-grain MR possibly originates from the fact that our sample itself is a finite random resistance network, whereas the classical model suggests that the positive MR of small finite random networks really depends on the particular network configuration [20].

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Fig. 3 Characters of MR. (a) Field dependence of the MR of intra-grain and inter-grain, showing non-saturating linear behaviour at 3.2K. (b) MR plotted as a function of B above a threshold field.

temperatures, respectively.

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(c) and (d) MR vs magnetic field measurements of intra-grain and inter-grain at different

We also observed weak localization (WL) derived negative magnetoresistance at low

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temperatures, and which is evident as a zero-field peak in magnetoresistance. Figs. 4(a) and 4(b)

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show the WL cusp of intra-grain and inter-grain at low magnetic field. The cusp depth decreases with increasing the temperature until it disappears at 50 K, confirming its quantum coherence origin. The graphene magnetoresistance corrected by WL in bilayer graphene can be analyzed using the following expression for the magnetoconductivity [50]: ℏ

()*

()*

()*

∆σ % = & '()* , − & '()* -.()* , + 2& '()* -()* -()* ,, +

+

+

/

/

∗

(3)

where F(x) = ln(x)+ψ(1/2+1/x), ψ(x) is the digamma function, 3 45 = (4De/ℏ)B and D is the diffusion constant. The coherence time τφ caused by inelastic scattering, is expected to reduce as the 12

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temperature is raised, while intervalley (intravalley) scattering time τi (τ*) derived from the defects and impurities should be largely temperature-independent. According to equation (3), the quantum correction depends not only on the dephasing time τφ but on elastic scattering times τi and τ*. Various inelastic (Lφ, phase-breaking) and elastic (Li, intervalley; and L*, intravalley) scattering

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45 45 lengths have the relation 6.7,9,∗ = :37,9,∗ . Here 3∗45 = 3; + 3<45 ，3<,; are the single valley

chirality-breaking and trigonal warping rates, respectively. Strong warping scattering effect without intervalley scattering (3∗45 ≫ 3745 ≫ 3945 ) makes the third term in Eq. (3) be suppressed while the first

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two cancel each other, so WL is destroyed. However, introducing some intervalley scattering (3∗45 ≫ 3745 ~3945) will restore WL, as it prevents the first two terms from cancelling and the first

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term dominates in small fields [24]. We will now see that it is exactly this situation that describes the experimental results. The WL curves we observed at low temperature are well fitted with the theory according to Eq. (3), as shown in Figs. S4(a) and S4(b) in the Supporting Information. The derived Lφ (Li) of intra-grain and inter-grain are ~428 nm (551 nm) and ~339 nm (498 nm),

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respectively. The extracted L* ~40 nm is insensitive during the curve fitting process. The fitting characteristics 67,9,∗ as three free parameters and their dependence on temperature are shown in figs. 4(c) and 4(d). Inter-valley scattering comes from atomically sharp defects, whereas intra-valley

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scattering arises from ripples and dislocations, as well as atomically sharp defects. Sharp defects in

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GBs act as a significant source of intervalley scattering, which is consistent with the relatively smaller value of Li in inter-grain compared with intra-grain. In short, our work has clearly shown that the GBs play an important role in quantum interference effect, which increase the intervalley scattering and reduce the phase-breaking length of CVD graphene.

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Fig. 4 Analysis of the transport environment. The relative magnetic conductance (∆G(B)=G(B)–

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G(0)，normalized by e2/h) of intra-grain (a) and inter-grain (b), plotted against the perpendicular low-field B, at various temperatures. Zero-field cusps, manifesting WLs, decayed with increasing temperature. Fitting parameters of intra-grain (c) and inter-grain (d), extracted from the WL theory

4. Conclusion

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respectively. The dashed lines are guides to the eyes.

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We have synthesized hexagonally shaped single-crystal bilayer gaphene grains on polycrystalline Cu foils. The distinct Raman D peaks at GBs suggest that there is a significant source of intervalley scattering, which gives prominent characteristics in the electronic transport measurements and allows us to locally explore the electronic behavior of individual graphene GBs at the nanometer scale. The metallic character of GB in the temperature dependence of resistivity was observed, and extracted GB resistivity reflects the effect of enhanced scattering at GB defect sites. We have performed magnetotransport measurements on graphene bicrystals that exhibit large 14

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linear MR at high fields due to inhomogeneous charge transport, decorated by WL effects at low temperatures. The GBs have been shown to impede electrical transport, suppress the magnetoresistance and enhance intervalley scattering in CVD graphene. However, graphene GBs can act as metallic nanowires to form building blocks for atomic-scale, all-carbon electronics, and

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are suitable for exploiting toward strong magnetic field detectors. Our study highlights the importance of GBs in CVD graphene and demonstrates potential applications in the future magneto-electronic devices.

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Acknowledgements

This work was supported by the National Key Projects for Basic Research of China (Grant No.

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2015CB921203), the National Key Research Programme of China (Grant No. 2016YFA0201004), the National Natural Science Foundation of China (Grant Nos. 51472113 and 11134005), the Natural Science Foundation of Jiangsu Province (Grant No. BK20180327), the Fundamental

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Research Funds for the Central Universities (Grant No. 021014380096), and the Scientific Foundation of Nanjing Institute of Technology (Grant Nos. ZKY201807, CKJA201807). Appendix A. Supplementary data

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References

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Supplementary data related to this article can be found at http://dx.doi.org/10.1016/j.carbon.

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