Letter pubs.acs.org/NanoLett
Magnitude and Origin of Electrical Noise at Individual Grain Boundaries in Graphene Vidya Kochat,*,† Chandra Sekhar Tiwary,‡ Tathagata Biswas,† Gopalakrishnan Ramalingam,§ Kimberly Hsieh,† Kamanio Chattopadhyay,‡ Srinivasan Raghavan,§,∥ Manish Jain,† and Arindam Ghosh†,∥ †
Department of Physics, ‡Department of Materials Engineering, §Materials Research Center, and ∥Centre for Nano Science and Engineering, Indian Institute of Science, Bangalore 560 012, India S Supporting Information *
ABSTRACT: Grain boundaries (GBs) are undesired in large area layered 2D materials as they degrade the device quality and their electronic performance. Here we show that the grain boundaries in graphene which induce additional scattering of carriers in the conduction channel also act as an additional and strong source of electrical noise especially at the room temperature. From graphene field effect transistors consisting of single GB, we find that the electrical noise across the graphene GBs can be nearly 10 000 times larger than the noise from equivalent dimensions in single crystalline graphene. At high carrier densities (n), the noise magnitude across the GBs decreases as ∝1/n, suggesting Hooge-type mobility fluctuations, whereas at low n close to the Dirac point, the noise magnitude could be quantitatively described by the fluctuations in the number of propagating modes across the GB. KEYWORDS: CVD graphene, grain boundary, 1/f noise, Hooge model, transmission probability
T
scale.1,15,18−27 Several microscopy studies have revealed the presence of atomically sharp GBs in graphene films obtained by CVD where the two grains are stitched together by either pentagon−heptagon or octagon−pentagon line defects depending on the misorientation angle between the two grains.19,28 These have been predicted to form localized states at the Fermi energy that resonantly backscatter the low-energy charge carriers.15 Aperiodic GBs have also been observed in some recent microscopic studies which are highly disordered/ amorphous where the disorder content can vary depending on the growth conditions.23,29,30 It was experimentally shown that the conductivity of such disordered GBs depend entirely on the interconnectivity of the grains which can be tailored using specific growth procedures.23 The scanning tunneling microscopy (STM) studies of disordered GBs revealed the presence of large potential barriers resulting in strong carrier scattering.29,30 The magneto-transport studies across a single GB displayed enhanced weak localization features in contrast to the measurements within a single grain thereby proving that the GBs also act as intervalley scattering centers in graphene.22 However, in spite of much transport and spectroscopic investigation on individual GBs in graphene, the impact of these GBs on intrinsic electrical noise, a key performance limiting factor in electronics, has not been investigated so far.
he graphene-based layered structure and its analogues have been an active topic of research due to their prospective applications in the field of sensing,1,2 ultrahigh frequency transistors,3 supercapacitors,4−6 and flexible and optoelectronic technologies.7−9 The applications envisioned for graphene require its large-scale production without compromising on the electronic quality which has resulted in the development of several growth techniques for the industrial scale production of graphene.9 Among these, the chemical vapor deposition of graphene on transition metals, especially Cu, has been vigorously pursued due to its many advantages over the other scalable techniques primarily owing to the ability to grow predominantly monolayer graphene films transferrable to any substrate of choice.10−12 The main challenge of the CVD technique is that the films grown are, in general, polycrystalline in nature due to the uncontrolled nucleation of graphene domains on the defect sites in Cu, followed by their growth and coalescence giving rise to grain boundaries (GBs). Although large single graphene grains have been prepared recently using CVD, their quality is still not at par with exfoliated graphene devices due to the presence of intragranular line defects and other structural defects.13,14 The GBs form a class of extended defects which break the lattice symmetry in graphene and modify the electronic structure locally.15−17 From the fundamental perspective, the GBs in atomically thin 2D materials present a new class of 1D topological defects which offer an ideal platform to tune charge and spin transport at the atomic © XXXX American Chemical Society
Received: October 17, 2015 Revised: December 2, 2015
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DOI: 10.1021/acs.nanolett.5b04234 Nano Lett. XXXX, XXX, XXX−XXX
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Figure 1. (a) SEM image of individual graphene grains grown on Cu (acale bar = 10 μm). (b and c) (i) Bright field TEM image of the GB, (ii) FFT pattern showing the misorientation angle between the two joining grains, and (iii) HRTEM image of the interface region aligned in a two-beam condition for Type I and Type II grains, respectively. (d) Comparative histogram of the interface thickness for both types of GBs. (e) Comparative histogram obtained from the FFT pattern showing the misorientation angle between the two grains. (f) HRTEM images showing the defected lattice at the GB region (left) and the perfect hexagonal lattice (right).
identification of individual grains. In order to understand the atomic structure of the GBs, a bright-field TEM imaging of the various GBs was performed, from which we observed two classes of GBs characterized by their widths and misorientation angles between the adjoining grains. These are shown in Figure 1b and c and have been termed as Type I and Type II GBs, respectively. A comparative histogram (obtained from a total of 50 GBs) of the interface thickness for both kinds of GBs shown in Figure 1d clearly indicates that Type I GBs are much narrower than the Type II GBs. The orientation relation between the two graphene grains forming the GB was obtained from the fast Fourier transform (FFT) of the TEM images. The FFT pattern for both kinds of interface and the misorientation angle between the two grains are marked in panel ii of Figure 1b and c. A comparative histogram using several such FFT data for both kinds of interfaces is shown in Figure 1e from which we can infer that the graphene grains which are highly misoriented form wider interfaces. To gain a better insight into the structural disorder at the GB, a detailed HRTEM analysis was performed across the interface region. The panel iii of Figure 1b and c shows HRTEM image of the Type I and Type II graphene interface regions aligned in two beam condition. It can be clearly seen that the Type II interface has a higher dislocation concentration as compared to the Type I interface. HRTEM images in Figure 1f clearly shows the defected lattice at the GB/interface (left panel) in comparison to the perfect hexagonal lattice (see right panel) in the interior of each graphene grain. Electrical measurements across individual GBs were performed using devices as shown in Figure 2a. The devices were prepared by optically identifying the GBs, followed by ebeam lithography and allowed us to carry out electrical transport measurements both within and across the GBs simultaneously. We have confirmed the presence of the GB using Raman mapping, where we have plotted the intensity of
The low frequency 1/f noise studies on exfoliated graphene devices have shown that the microscopic origin of the conductivity fluctuations can be traced to the correlated number−mobility fluctuations arising from the dynamic charge carrier exchange between the graphene channel and the traps in the oxide substrate/adsorbed functional groups. The magnitude of these fluctuations depends on the electrostatic screening of the charged traps which is intrinsically related to the bandstructure and layer number in graphene.31−44 Given that GBs are not only additional scattering centers, but also modify local band structure, the nature and magnitude of noise at the graphene GBs can be drastically different from noise in graphene transistors built on crystalline exfoliated flakes. In this work, we have measured the 1/f noise across individual GBs in graphene. We have obtained two different classes of disordered graphene GBs, which are distinguishable based on their misorientation angle and GB width. Increasing the width of the disordered boundary region reduces the measured conductivity and increases the 1/f noise magnitude. Since the GBs can be an unavoidable consequence of large area graphene growth, our work emphasizes on designing growth procedures which should focus on reducing the width of the disordered intergrain interfaces to enable low-noise electronic/ sensing applications. The graphene grains studied in this work were grown using the CVD technique by the thermal decomposition of methane gas in the presence of H2 gas on Cu foil enclosures. These are then transferred to holey-C grids for TEM characterization or Si++/SiO2 substrates for electronic transport measurements employing a polymer-assisted transfer technique.10 The individual graphene grains and GB regions were characterized using a combination of optical, SEM, and TEM microscopy (for details, see Supporting Information). The SEM image in Figure 1a shows the graphene grains on Cu foil where their growth was halted before the formation of a continuous film to enable B
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GB is distinctly lower in comparison to the Type I GB as shown in Figure 2d, where we have shown the σGB from two Type I and two Type II devices. The low frequency electrical noise in the single GB graphene devices were measured in vacuum in a standard 4-probe configuration. The time-dependent voltage fluctuations across the GB illustrated with a Type I device (inset of Figure 3a)
Figure 2. (a) Optical micrograph of the Type II GB device showing the scheme for intragrain and intergrain resistance measurements (scale bar = 5 μm). The right panel shows the Raman D-map of the region outlined in red confirming the presence of GB. (b) The sheet resistance at 300 K of the intragrain (SG) and intergrain (GB) regions of the devices. (c) ρGB as a function of n is plotted for Type I and Type II GBs at three different temperatures. (d) GB conductivity (σGB) at 300 K in the hole regime for two devices each containing the Type I and Type II GBs. Figure 3. (a) Normalized power spectrum at various densities obtained from the time series of voltage fluctuations shown in the inset. (b) Schematic showing the potential drop across the GB and single crystalline graphene region between the voltage probes. (c) The noise parameter (A × SV/V2) as a function of gate voltage for the Type I and Type II devices at 300 K. The shaded region highlights the dip in noise in the Dirac point regime.
the D-peak for the area outlined (red) in the optical micrograph. The increased D-peak intensity is an indication of the large intervalley scattering arising from the GBs.22 The four-terminal resistance measurements at temperatures varying from 300 K down to 4.2 K were done in a variable temperature cryostat, while the ultralow temperature measurements were performed inside a Janis 3He-cryostat. The intragrain and intergrain sheet resistances (R□) at 300 K for the Type I and Type II GB devices are shown in the two different panels in Figure 2b. The resistivity of the particular GB can be calculated by considering the total resistance (R′) of the measured region as a sum of the resistance of the single grain region and the additional resistance induced by the GB, which is expressed as ρ L R′ = ρ□ + GB (1) W W where ρ□ is the intragrain resistivity, L and W the length and width between the voltage probes, and ρGB is the resistivity per micrometer length of the GB. In Figure 2c we have plotted ρGB for the Type I and Type II GBs as a function of gate voltage, VG (measured from the Dirac point, VD) at different temperatures. We find that ρGB of Type II GB at Dirac point is larger by an order of magnitude at low temperatures in comparison to the ρGB of Type I GB. This confirms that the Type II GBs pose a severe barrier to the transmission of low energy carriers, which can be attributed to their higher dislocation density (Figure 1c), and confirmed by density functional theory calculations (Supporting Information). Also STM studies have reported the formation of n-type inversion channels across GBs in a hole-doped graphene lattice and have attributed this to the phenomenon of self-doping.30,45 This arises due the presence of localized defects and the absence of electron−hole symmetry resulting in a charge transfer between the GB and the clean graphene regions.16 This formation of p−n−p or p′−p−p′ junctions at the GBs could also explain the lower conductance of the GB regions. Even at room temperature, the minimum conductivity per micrometer length of the GB for the Type II
show 1/f- type power spectrum at all carrier densities (Figure 3a). Here we have plotted the normalized power spectral density (PSD), given by SV/V2, where V (= VTGB) is the potential difference between the voltage probes placed on either side of the GB (schematic in Figure 3b). In order to compare the noise levels of the Type I and Type II GB devices at room temperature, we evaluate the noise parameter, which is the PSD normalized by the area, A, of the measured intragrain (SG) and intergrain (GB) regions between the voltage probes (Figure 3c). The noise in the GB regions, for both the Type I and Type II GBs, are significantly larger than the SG regions implying that the GBs can have serious detrimental effect on multidomain CVD-grown graphene devices in room temperature operation. The marked asymmetry in the noise magnitude in the hole and electron doped regimes may be attributed to the asymmetric carrier scattering by charged impurities.44 At 300 K, the noise in both types of devices shows a weak dip at the Dirac point for the SG and GB regions. Such a nonmonotonic noise behavior as a function of gate voltage has also been observed previously in exfoliated single layer graphene FETs31,35,36,39 and has been attributed to the inhomogeneous spatial charge distribution arising from the formation of electron−hole puddles at low densities in the presence of charged traps in the substrate and adsorbed functional groups on graphene.31−39,41−43,46−48 In order to characterize the noise levels of the different types of GBs, we need to estimate the noise arising from the GB part alone from the total measured noise in the intergrain region. As depicted in the schematic in Figure 3b, the total measured voltage drop (VTGB) in the intergrain region is the sum of the voltage drop across the single grain area (VSG) and the voltage C
DOI: 10.1021/acs.nanolett.5b04234 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters drop across the GB region (VGB). Assuming that the noise arising from the single grain part (SGV ) in both the SG and intergrain regions remains the same, the noise from the GB G (SGB V ) can be obtained by subtracting SV from the total T 2 measured noise (SV). The normalized GB noise, SGB V /VGB is then given by SVGB 2 VGB
2 ⎛ VSG ⎞2 ηSG VSG ⎞ SVT ⎛ = ⎜1 + ⎟ −⎜ ⎟ T 2⎝ VGB ⎠ ⎝ VGB ⎠ ASG VGB
which may arise from, for example, local redistribution of trapped charges in the substrate.31 This n -dependence is more scattered in the Type II GBs, which is probably the result of larger statistical variation of disorder within the GB region. For a microscopic understanding of the observed magnitude of noise at the GB, we consider the low n regime, where the GB can be considered to be a tunnel barrier with width dependent transmission coefficient Γ (see schematic of Figure 4b). From the Landauer formalism, the GB conductance is given by52 GGB = (2e2/h)MΓ, where M = kFW/π is the number of transverse modes across the GB of width, W. Since the screening of the trapped charges is weak at low n, individual charge trapping event (and/or reorganization of trapped charge) can be assumed to directly result in the fluctuation in M, such that ⟨δG2GB⟩ = (2e2/h)2Γ2⟨δM2⟩ = (2e2/h)2Γ2⟨(δnT)2⟩ ≃ (2e2/ h)2Γ2.53 Indeed, as shown in Figure 4c, we find the experimental conductance noise ⟨δG2GB⟩ at both types of GB at low n agree closely with Γ2, where the latter was evaluated directly from the GB conductance (here, δnT ∼ 1 is the fluctuation in the number of trap states). At larger n (or Fermi energy), screening of the trapped charges weakens this effect, and noise is determined by the fluctuations in the scattering potential (hence mobility fluctuations) within the GB. Finally, to compare the noise levels of the GBs with that of SG single crystalline graphene regions, we compare SGB V with SV ′, SG SG where SV ′ = (LGB/L) × SV is the voltage noise generated within the grain from a region of the same length as the GB, LGB (L is the length of the SG region between the voltage probes). This is plotted in Figure 5a for the Type I and Type II
(2)
where STV /(VTGB)2 is the normalized noise measured in the intergrain region between the voltage probes shown in Figure 3b, ASG is the area of SG region between these voltage probes and ηSG is the noise parameter of the SG region estimated independently from the noise measurement in the adjacent 2 grains. The SGB V /VGB for Type I and Type II GBs in the hole doped regime are plotted in Figure 4a and b, respectively, as a
2 Figure 4. (a) The normalized GB noise, SGB V /VGB for the Type I and Type II GBs, respectively, as a function of hole density at different temperatures. The dotted line denotes nC, which is the characteristic 2 density scale below which SGB V /VGB almost remains constant. (b) Schematic showing the GB as a potential barrier with reflection coefficient, 9 and transmission coeffiecient, Γ, where the number of transverse conduction modes can be tuned as a function of carrier density. (c) The comparison of the experimentally measured noise near the Dirac point in the Type I and Type II GBs and the magnitude of conductance fluctuations from the calculation of Γ2.
function of hole density n. The GB noise is maximum at low n (close to the Dirac point) but decreases with increasing n above a characteristic scale nC that is smaller (nC ∼ 5 × 1011/cm2) for Type I GB than Type II GB (nC ∼ 2 × 1012/cm2). For both 2 2 GBs, we observe that SGB V /VGB at n > nC follows a 1/n dependence at low T, which gradually changes to a 1/n behavior at higher T, suggesting the mechanism of noise at low temperatures to be different from that at higher T. The ∼1/n2dependence of noise at low T is suggestive of trapping− detrapping noise49 that involve exchange of conduction electrons between the channel and localized trap states. In the present case, these trap states could be the oxide traps, GB induced localized states or the states associated with the adsorbed functional groups at the GB due to the high chemical sensitivity of GBs in graphene.1,50 The ∼1/n-dependence of noise at higher T, on the other hand, indicate Hooge-type mobility fluctuations to be the dominant source of noise,51
Figure 5. (a) Voltage noise (SV) calculated from the GB part alone, SG SGB V , and an area of equivalent width from SG region, SV ′ = (LGB/L) × SG , for the Type I and Type II GB devices. (b) Ratio of SGB SSG V V and SV ′, showing the huge increase in noise from the GB.
GB devices as a function of carrier density at 300 K, with LGB = 2 and 10 nm for the Type I and Type II GBs, respectively. We observe that the voltage noise in the GB region is several orders of magnitude larger that the noise from the equivalent SG region. The ratio of these GB and SG noise magnitudes shown in Figure 5b clearly highlights the two main results of this work, the first important result being that the noise arising from GB in graphene is 3000 to 10 000 times larger than the single crystalline regions at room temperature and that secondly, the D
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Type II GBs which also showed higher dislocation density along their width are noisier than the Type I GBs. In summary, we have investigated the 1/f noise arising from GBs of varying thicknesses in polycrystalline graphene and find that the noise magnitude in these devices are strongly dependent on the disorder level and thickness of the GBs. We also observe that, while the noise at higher densities can be explained by a correlated number and mobility fluctuation model, the noise at low densities where the GB has negligible transmission probability arises from the fluctuations in the total number of transverse modes across the GB. While the additional noise due to GBs is undesired for many low noise applications, it can be potentially exploited in sensor-based technologies.
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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.5b04234. Device characterization procedures and computational details (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We acknowledge financial support from the Thematic Unit of Excellence under Nanomission, Department of Science and Technology, Government of India. C.S.T. and K.C. would like to acknowledge AFMM, IISc for microscopy facilities. V.K., T.B., and K.H. thank CSIR for financial support.
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