f Noise at Multiple Dirac Cones in hBN Encapsulated

Jan 14, 2016 - Here, we present the low-frequency 1/f noise measurements at multiple Dirac cones in hBN encapsulated single and bilayer graphene in ...
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Tunability of 1/f Noise at Multiple Dirac Cones in hBN Encapsulated Graphene Devices Chandan Kumar,† Manabendra Kuiri,† Jeil Jung,‡ Tanmoy Das,† and Anindya Das*,† †

Department of Physics, Indian Institute of Science, Bangalore 560012, India Department of Physics, University of Seoul, Seoul 130-742, Korea

‡

S Supporting Information *

ABSTRACT: The emergence of multiple Dirac cones in hexagonal boron nitride (hBN)−graphene heterostructures is particularly attractive because it offers potentially better landscape for higher and versatile transport properties than the primary Dirac cone. However, the transport coefficients of the cloned Dirac cones is yet not fully characterized and many open questions, including the evolution of charge dynamics and impurity scattering responsible for them, have remained unexplored. Noise measurements, having the potential to address these questions, have not been performed to date in dual-gated hBN−graphene−hBN devices. Here, we present the lowfrequency 1/f noise measurements at multiple Dirac cones in hBN encapsulated single and bilayer graphene in dual-gated geometry. Our results reveal that the low-frequency noise in graphene can be tuned by more than two-orders of magnitude by changing carrier concentration as well as by modifying the band structure in bilayer graphene. We find that the noise is surprisingly suppressed at the cloned Dirac cone compared to the primary Dirac cone in single layer graphene device, while it is strongly enhanced for the bilayer graphene with band gap opening. The results are explained with the calculation of dielectric function using tight-binding model. Our results also indicate that the 1/f noise indeed follows the Hooge’s empirical formula in hBN-protected devices in dual-gated geometry. We also present for the first time the noise data in bipolar regime of a graphene device. KEYWORDS: Graphene, Moire pattern, 1/f noise, band gap opening, screening, bipolar regime

T

potential provided by the hBN gives a superlattice modulation to the graphene band structure.21−23 It is demonstrated that the energy and momentum position of the CDs, the corresponding Dirac Fermion velocity, Dirac mass can be simultaneously controlled by the relative orientation between the graphene and hBN.15 Interestingly, it has been empirically observed that the resistivity of CD is substantially reduced compared to that of the primary Dirac (PD) cone.16,17 Similarly, the enhancement of resistivity at PD in gapped BLG has been reported.24,25 However, despite extensive research in SLG and BLG, the impurity scattering mechanism at CDs as well as PDs has remained unidentified, and thus the functionality of SLG and BLG could not be explored further. Low-frequency 1/f noise is a complementary and versatile probe to study the charge dynamics, density fluctuations, and dielectric screening that contribute to the charge transport properties but cannot be directly accessed by resistivity measurements. Low frequency 1/f noise is characterized by an inverse dependence of current power spectral density on frequency SI ∝ 1/fβ, where β ≈ 1. For various semiconductor

he Dirac-like dispersion of graphene is both an advantage and disadvantage for practical applications. The advantages of graphene mainly stem from its Dirac cones that renders extremely high charge mobility,1−7 long-ranged ballistic transport,1−7 and enhanced thermal conductivity8−10 among others. Functionalizations of these properties, however, rely on material flexibility and enhanced tunability where the impurity scattering and Coulomb interaction can be monitored desirably. The simplicity of the graphene band structure thus poses a challenge to the funtionalization of single layer graphene (SLG) as well as bilayer graphene (BLG). For example, it has been reported both experimentally11,12 and theoretically13,14 that SLG and BLG are highly sensitive to external perturbation such as charge impurities or adsorbants that degrades its performance. It has remained a long-sought goal to obtain experimentally accessible Dirac cones where impurity scatterings and Coulomb interaction can be effectively minimized or tuned without impairing the essential functional properties of graphene. The discovery of graphene and hexagonal boron nitride (hBN) heterostructure has introduced versatile tunabilities of Dirac band structure properties, including cloning of Dirac cone into multiple numbers, band velocity renormalization, and Dirac mass production.15−20 The electronic and transport properties of the cloned Dirac (CD) cones has been studied extensively.15−20 The weak periodic © XXXX American Chemical Society

Received: October 9, 2015 Revised: December 29, 2015

A

DOI: 10.1021/acs.nanolett.5b04116 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. (a) Schematic of the dual-gated SLG device, showing the emergence of moire pattern for hBN (red) on SLG (blue). (b) Theoretically calculated dispersion relation for graphene, showing the emergence of cloned Dirac points in the presence of weak hBN periodic potential. (c) Left: the electronic band dispersion of prestine BLG. Middle: band gap opening due to resulting displacement field (δD = 0, D̅ ≠ 0). Right: shift of Fermi energy due to doping (δD ≠ 0, D¯ = 0). (d) Optical image of hBN encapsulated SLG device. Inset shows the optical image of BLG sitting on hBN. Scale bar: 10 μm.

devices,26 carbon-nanotube27,28 and indium arsenide nanowires,29,30 the 1/f noise follows the Hooge’s empirical formula SI I

2

where

= SI I2

SV V

2

=

SR 2

R

=

αH fN

accounting the extraneous sources such as contacts, ungated part as well as the intrinsic mechanism like dielectric screening. In this report, for the first time we carry out the 1/f noise measurements at CD as well as PD in a dual-gated (top and back gate) bipolar FET device using hBN-SLG-hBN as well as hBN-BLG-hBN heterostructures. With our dual-gated geometry, we are able to separate out the actual 1/f noise contribution of the graphene channel from the ungated part as well as the contact noise. Our results show that the 1/f noise of SLG and BLG indeed follows the Hooge’s empirical formula. Surprisingly, the noise amplitude is seen to decrease by two orders of magnitude with carrier concentration away from the PD and at CD the noise is suppressed. We benchmark our results with a systematic study in BLG, where the 1/f noise amplitude at PD has been tuned as a function of band gap opening by applying transverse electric field with the combination of top and back gates. Our results show that the noise amplitude increases by more than an order of magnitude due to the gap opening by 40 meV. The results are explained with the calculation of the momentum resolved dielectric function calculations using realistic tight-binding model for the graphene/hBN device. Our combined studies of theory and experiment using dualgated geometry help to pin down the precise mechanism of the noise source in graphene at PD and CD, arising mainly from the charge impurities. Figure 1a shows the schematics of dual-gated hBN-SLG/ BLG-hBN devices. The bottom 300 nm SiO2 acts as a global back gate (VBG) while the top hBN acts as a local gate (VTG). The heterostructures are fabricated using dry transfer technique.6 First, a thin hBN (∼10−20 nm) flake is transferred on top of SiO2 followed by transfer of SLG or BLG on the bottom hBN and at the end it is covered with an another thin top hBN (∼10−20 nm) flake, which serves as top gate. Source, drain, and gate contacts were made by electron beam lithography (EBL) followed by thermal evaporation of Cr/Au

(1)

is the normalized noise amplitude, αH is Hooge

parameter, and N is the total number of charge carriers. Given that 1/f noise mainly originates from the combination of carrier density fluctuations and mobility fluctuations by charge trapping and detrapping mechanism between the materials and substrate, it gives a direct access to the both inelastic and elastic scatterings properties. With scientific and technological interests, 1/f noise has been studied extensively in SLG and BLG based FETs.31−43 Most of the measurements31,32,35−42 have been done using a SiO2 back gate. Earlier studies on SLG and BLG have revealed unusual carrier concentration dependence of the 1/f noise. It is shown that the noise is minimum at the Dirac point and increases with carrier concentration with a “V’ or ‘M”-like shape.31,35,37−39,42 More interestingly, the apparent deviation from the Hooge’s empirical formula in graphene has attracted lot of attention and has been attributed to the effect of spatial charge inhomogeneity by charge puddles,35,41,43 inhomogeneous trap distribution,34,35,39,43 influence of contacts and edges,32,33,44 interplay between the long and short-range scattering mechanisms.37,39 Very recently, 1/f noise measurement has been reported in graphene in suspended geometry44 as well as on hBN substrates45,46 and observed much lower noise compared to the SiO2 substrate, and the noise amplitude remains almost independent of the carrier concentration.46 Despite extensive studies there is still no consensus on the origin of 1/f noise in graphene. A more comprehensive study is required in dual-gated geometry to address the 1/f noise anomaly in graphene based devices by B

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Figure 2. Two-dimensional plot of resistance for SLG1 as a function of top and back gate at (a) 77 K and (b) 4.2 K. (c) (top panel) Resistance plot as a function of VTG at VBG = −30 V and (bottom panel) as a function of VBG at VTG = 4 V. Two-dimensional plot of resistance for BLG as a function of top and back gate at (d) 77 K and (e) 4.2 K; the diagonal dashed arrow indicates δD ≠ 0, D̅ = 0 direction. (f) Cut lines for several VBG from −32 to 32 V.

(5 nm/70 nm). In the case of SLG, the edge of the top hBN layer was precisely aligned with the graphene edge and annealed at 300 °C to have Moire pattern.20 The details of method are given in the Supporting Information (SI). The SLG and BLG was confirmed by Raman spectra as shown in the SI. The Moire pattern sample (SLG device) is characterized by Moire wavelength, λ.15,16 From the transport measurement, we find λ ∼ 9 nm in our device. Figure 1b shows the energy dispersion of SLG with λ = 9 nm using tight binding calculation. It can be seen from the figure that the emergence of three in-equivalent CD points at E ∼ −0.25 eV. In BLG, the combination of back and top gates allow us to independently control the carrier concentration and the electronic band gap under the top-gated region. The applied electric displacement field DT and DB resulting from top and back gating is given by

DT =

th ϵt(VTG − VTG ) dt

and DB =

th ϵb(VBG − VBG ) , db

Figure 2a,b shows the 2D color plot of the resistance as a function of VBG and VTG for hBN-SLG1-hBN device at 77 and 4.2 K, respectively. The most prominent feature is the two diagonal lines which are parallel to each other. At 77 K (Figure 2a) only one diagonal line is prominent that corresponds to the PD of graphene. The additional diagonal line becomes prominent at 4.2 K (Figure 2b) corresponds to the CD. Figure 2c shows the gate response as a function of VTG for a fixed VBG and vice versa along the dashed horizontal and vertical lines in Figure 2a,b. The two resistance peaks are clearly visible with VTG and becomes more prominent at lower temperature. The VBG response at 77 K shows a resistance peak at −12.5 V. However, the VBG response at low temperatures is limited by the conductance fluctuations, which does not depend on the VTG. This could be due to the effect of disorders near the contact as well as untopgated part, which has been seen earlier.49,50 From the slope of the diagonal lines, we calculate the relative capacitance coupling of the top gate with respect to the back gate to be ∼11. It can be seen from Figure 2c that PD and CD are separated by ΔVTG ∼ 6 V (Δn ∼ 1012 cm−2) . Using the relation between carrier concentration and Moire 8 wavelength,16 Δn = 2 , we calculate λ ∼ 9 nm, which

where ϵt and ϵb are

the dielectric constants, dt and db are the thickness of dielectric th layers, and Vth TG and VBG are the charge neutrality points (CNP). The displacement field has primarily two effects as following. The net doping is determined by δD = DB + DT. Nonzero δD leads to the doping of electrons or holes under the top gated region. On the other hand D = (DB − DT)/2 leads to nonzero band gap.25,47 By fixing δD = 0 and varying D̅ or vice versa we can tune either the band gap while keeping the EF at CNP or tune the EF while keeping zero band gap, which has been shown schematically in Figure 1c. Figure 1d shows the optical images of hBN-SLG/BLG-hBN devices. All the measurements are performed at 77 and 4.2 K in a home-built dipstick using standard lock-in technique. The conductance fluctuations were measured by a NI USB 6210 DAQ card after amplified by a home build current preamplifier having a gain of 107, voltage noise of 6 nV/ Hz and current noise of 50 fA/ Hz .48

3λ

corresponds to energy separation of ∼250 meV.15 However, we only observe the CD for hole side as predicted theoretically15 and observed experimentally.15 We note that the presence of CD is due to the alignment of top hBN with graphene. However, there could be CD at higher energy due to the bottom hBN, which was not accessible in our experiment due to dielectric breakdown. We model the resistance data as follows. The total resistance, RT, between source and drain is given by RT = Rch+ RL, where Rch is the channel resistance (under the top gate) and RL is the resistance coming from the leads (untopgated part and contacts). Rch depends on both top-gate and back gate whereas C

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Figure 3. (a) Normalized noise spectral density as a function of frequency at 4.2 K for different set of VTG in BLG at VBG = −32 V, the inset shows the value of β as a function of VTG. (b) The resistance and noise amplitude as a function of VTG in SLG for VBG = −25 V and (c) in BLG for VBG = −32 V. The solid line and the filled circle with line corresponds to the resistance and noise data, respectively. (d) Noise amplitude measured in BLG along the band gap opening direction (δD = 0, D̅ ≠ 0). (e) Noise amplitude in BLG along the zero band gap direction (δD ≠ 0, D̅ = 0).

RL depends on only back gate. The total resistance can be written as51 RT = RL +

even though we open a gap of 40 meV the channel does not become insulating at 4.2 K due to the presence of tail states in the channel.47 Figure 3a shows the typical power spectral density of conductance fluctuation of the SLG/BLG devices for several VTG at 4.2 K and it remains 1/fβ nature for a wide range of frequency from 0.1 to 100 Hz. The detail of the fluctuation measurement has been described in the SI. As seen in the inset of Figure 3a, the β remains close to 1 around the Dirac point. The integrated noise amplitude A of SLG as a function of VTG is shown in Figure 3b. It can be seen that noise amplitude (A) is maximum at the PD and decreases with carrier concentration. On the contrary A is minimum at the CD and it increases with carrier concentration. A natural question arises whether the noise reduction is related to the tiny band gap opening at CD. This possibility can be excluded by comparing the evolution of noise for BLG as a function of band gap (Figure 3c,d). For BLG, A decreases by more than two orders of magnitude with carrier concentration (Figure 3c) Figure 3d shows how A changes with band gap opening keeping EF at CNP. It can be seen that with the band gap of ∼40 meV the noise amplitude increases by ∼15 times compared to zero band gap. On the other hand, the A decreases along the zero band gap direction (dashed diagonal line in Figure 2e) shown in Figure 3e. We have also carried out noise measurements on another hBN-SLG2-hBN device at 77 K to investigate the effect of bipolar (n−p−n/p−n−p) regime on 1/f noise. The device has mobility of 15 000 cm2 V−1 s−1 and δn ∼ 5 × 1010 cm−2 (SI).

L TG 2 Weμ δn2 + nch

(2)

where W, LTG, and μ are the width, length, and mobility of the channel under the top gate. The carrier concentration of the C (V

− V th ) + C (V

− V th )

channel is nch = TG TG TG e BG BG BG and δn is the charge inhomogeneity. The δn of our channel is ∼8 × 1010 cm−2 (see SI for the details), which is more than 10−20 times smaller than the graphene on SiO2 devices.35,51 Using eq 2 we fit the resistance data (see the SI) and obtain the mobility of the channel around the PD and CD to be ∼9000 and 25 000 cm2 V−1 s−1, respectively. Figure 2d,e shows the 2D resistance plot as a function of VBG and VTG for hBN-BLG-hBN device at 77 and 4.2 K, respectively. We observe only one diagonal line, which corresponds to the CNP of BLG under the top gate region. It can be seen from Figure 2e that the resistance (at 4.2 K) increases by ∼15 times along the CNP indicating the band gap opening in BLG. This can be be clearly seen in Figure 2f by plotting the resistance as a function of VTG for several VBG. The maximum D in our device is ∼0.4 V/nm, which corresponds to a band gap of ∼40 meV.25 On the other hand, the dashed diagonal arrow in Figure 2e indicates the zero band gap direction (D = 0 and δD ≠ 0). The BLG device has μ ∼ 28 000 cm2 V−1 s−1 and δn is ∼6 × 1010 cm−2 (see SI). We note that D

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Figure 4. (a) Two-dimensional plot of resistance for SLG2 as a function of top and backgate at 77 K. (b) Resistance as a function of VTG for different values of VBG. (c) Two-dimensional plot of A as a function of VTG and VBG. (d) A in log scale as a function of VTG for different values of VBG.

Figure 5. Noise amplitude as a function of VTG at (a) PD, (b) CD for SLG1, and (c) for BLG. The dashed green line, dashed-dot blue line, and red line are the noise contributions coming from contact-lead, channel, and the total noise, respectively.

(δn). As a result, any charge fluctuations due to trapping− detrapping will increase (decrease) the size of electron puddles (hole puddles) or vice versa. Thus, some part of the graphene conducts more but other part conducts less. Therefore, total current remains constant and noise is minimum.35 With Fermi energy shift, one type of puddle grows compared to other one and noise increases until the channel has only one type of carrier (electron or hole) and afterward noise starts to decrease with carrier concentration as expected for long-range Coulomb scattering.37 In the case of hBN protected dual-gated device, the trap charges are in both the hBN layers52 as well as at the interface of bottom hBN and SiO2 substrate. It is the latter one that gives more inhomogeneity in the device. At higher VBG, the trap charges between the bottom hBN and SiO2 will be screened, and now if we approach the Dirac point of the middle part of our device (under the top gate region) by VTG the noise will be determined by the trap charges mainly in top hBN layer. As mentioned earlier, the δn in our device is ∼5 × 1010 cm−2, which is ∼20 times smaller compared to the graphene devices on bare SiO2. As a result, the effect of in-homogeneity is not observed in our noise measurement and we probe close to the true Dirac point. The noise decrement with carrier concentration proves the long-range charge impurities are the main source of noise. We should mention that noise measurement with back gate has always uncertainties about the effect of contact that changes with the back gate voltage. Therefore, by measuring the noise as a function of VTG by keeping VBG fixed we can figure out the noise contribution coming from the true channel (under the top gate) compared to the lead (untopgated part and contact). In order to understand the noise data as a function of VTG in n−p−n or p−n−p geometry, we use the following model, which has been used for semiconductor26 and nanowires.29 Considering the noise contributions coming from the channel

Figure 4a,b shows the 2D resistance plot and cut lines for several VBG, respectively. Figure 4c shows the 2D plot of noise amplitude A in log scale (for linear scale see SI) whereas the noise cut lines as a function of VTG for several VBG are shown in Figure 4d. The diagonal line in Figure 4c shows the noise maxima at the Dirac point under the top gate part, which exactly follow the diagonal line in the 2D resistance plot (Figure 4a). It can be clearly seen from Figure 4d that the magnitude of noise in dual-gated SLG2 device decreases with carrier concentration (as a function of VTG) and in fact it changes by 2 orders of magnitude whenever the untopgated part is highly doped (at higher VBG). However, near about the Dirac point of untopgated part (VBG = −0.66 V) the noise amplitude barely depend on VTG, as seen in Figure 4d. It should be also noted that A changes very weakly (less than two times) as a function of VBG (at VTG = 0), as seen in Figure 4c,d, which is very similar to hBN protected back-gated graphene devices.44,45 It can be seen from Figure 4c,d that the noise is symmetric around the Dirac point (as a function of VTG) like the resistance plot. There are no significant changes from unipolar to bipolar transition (n−n*−n to n−p−n or p−p*−p to p−n−p) even though the potential barrier height changes by ∼400 meV from unipolar to bipolar regime (for details see SI). This could be the fact that graphene has Klein tunneling.1 We want to note that in some literatures45,46 A × area has been quoted to specify the noise performance for different devices. For our hBN-SLG2-hBN device at 77 K, A × area is 1 × 10−8 μm2, which is smaller than ref 45 and 46, although those measurements are done at room temperature. We will now discuss the origin of noise in hBN protected graphene devices. The fluctuations of current with time in graphene devices on SiO2 substrate are originated due to trapping-detrapping mechanism of charges in SiO2. Near the Dirac point of graphene the conduction happens through the charge puddles of electron and hole due to inhomogeneity E

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Figure 6. (a) Total DOS for SLG/hBN. (b) Momentum averaged dielectric function (normalized to noninteracting dielectric constant ϵ0 as a function of VTG, modeled by rigid band shift of the chemical potential). (c,d) Momentum dependence of ϵ/ϵ0 is plotted in the first quadrant of the Brillouin zone for two representative VTG Fermi energies, marked by vertical dashed lines in (b).

Hooge’s empirical formula for noise is indeed applicable for 2D SLG- and BLG-based dual-gated devices, once the contributions from contacts and ungated part are properly included. Next we discuss the theoretical calculations to explain the surprising reduction of noise at the CD, that is, the reduction of the αH parameter in eq 1. The electronic structure of the graphene/hBN is modeled within realistic multiband tightbinding approximation with the tight-binding parameters fitted to the density-functional theory result.22,23,53 We account for the present device parameters of graphene/hBN orientation angle of θ = 1.15, and the energy separation between the PD and CD is about 250 meV, which is adjusted by the tightbinding parameter t = −4.5 eV. The band dispersion and the superlattice Dirac cone formation is shown in Figure 1b, and the corresponding density of states (DOS) is shown in Figure 5a. The weak periodic potential of the hBN opens a negligibly small band gap at the PD, which is almost invisible in the DOS plot due to finite impurity broadening, while an observably direct band gap opens at the CDs. Yet, a finite DOS arises at the CDs22,53 due to vanishing indirect band gap between the CDs as also seen by tunneling measurements.15 We calculate the momentum dependence of the dielectric constant ϵ(q, ω = 0) due to Kanamori-type charge screenings within the random-phase approximation (RPA)14 ϵ(q) = 1 + Vqχ(q). Here Vq is the long-range Coulomb interaction, and χ(q) is the noninteracting Lindhard susceptibility. The momentum averaged ϵ in Figure 5b shows a minimum at PD and then increases quadratically on both sides. To make a quantitative comparison, we indicated the value of ⟨ϵ⟩ at CD and at around EF = −0.03 eV at which the corresponding DOS in Figure 5a is the same. Despite the same DOS, we see that the ⟨ϵ⟩ increases by about 6 times in CD. This is because of the presence of larger Fermi surface pockets at CD compared to the PD. We present momentum resolved ϵ in Figure 5c,d at the two representative energy scales. We see that in both cases, the screening is dominated near q ∼ 0, and also at Q that connects between nearest Dirac cones, giving a hexagonal shape. At CD, the overall ϵ profile is similar, except that here the amplitude is higher as well as the signature of reduced Brillouin zone is evident. These results indicate that despite the similar charge

(Sch) and lead (SL) are uncorrelated, we can write the total noise (ST) as30 Sch SL ST = + , RT2 (R ch + RL)2 (R ch + RL)2

where

RT = R ch + RL (3)

2 αHR ch

With VTG, only Sch ( ) and Rch will change. Far away from N the Dirac point, the channel (under the top gate) will be highly doped compared to untopgated part. Thus, Rch ≪ RL, Sch ≪ SL S and eq 3 reduces to a constant value of ∼ RL2 (independent of L

VTG), as can be seen in Figures 3b,c and 4d. The value of the constant changes for different back gate voltages (Figure 4d) as well as from one device to other device. Using that constant and the experimental resistance value (RT vs VTG plot) we generate the noise contribution coming from the second part in eq 3 (LN), which increases with carrier concentration as shown by dashed green lines in Figure 5a,b. Similarly, the first part in α R2

eq 3 (CN) has been evaluated using Sch = HN ch and RT vs VTG plot, which decreases with carrier concentration as shown by dashed-dot blue lines. The total normalized noise (TN = CN + LN) is shown in solid lines. It can be clearly seen from Figure 5a,b that the model-generated total noise matches well with the experimental data with only adjusting parameter, αH. For BLG, αH ∼ 10−4 while for SLG1 at PD αH ∼ 10−3. The lower value of αH in BLG reflects that noise is lower compared to SLG1 as reported earlier.31 However, from Figure 5c it can be seen that for CD of SLG1 the model generated noise with αH ∼ 10−3 (black solid line in Figure 5c) does not match the experimental data. The increment of noise with carrier concentration at CD can be explained either by inhomogeneity or by the dominance of LN over the CN. The effect of inhomogeneity is ruled out in hBN protected graphene device as discussed earlier. The noise at CD is fitted well with αH ∼ 10−4 as shown by red solid line in Figure 5c because of the dominance of LN over CN. The lower value of αH at CD as compared to PD in SLG1 indicates lower noise near CD, which has practical application. The physics is due to different screening properties as discussed in the next paragraph. These results and our analysis indicate that the F

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Letter

Nano Letters

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screening profile, its amplitude is enhanced at CD, which effectively decreases the scattering from charge impurities and as a result reduces the noise amplitude. In summary, we have utilized the hBN encapsulated dualgated graphene devices to extract out the true 1/f noise contribution of the graphene channel. Our data shows that 1/f noise in graphene devices decreases by more than two orders of magnitude with carrier concentration. The reduction of noise with carrier concentration and lower value of noise at CD with theory calculation indicate that the main sources of noise are the long-range charge impurities. Our data indicates that there is no significant effect of potential barrier on 1/f noise in graphene n−p−n junction. Our finding with tunability of 1/f noise by two orders of magnitude will help to design the future graphene based devices to have best signal-to-noise ratio.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b04116. Fabrication details, Raman spectroscopy of SLG and BLG, charge inhomogeneity and mobility calculation, and 1/f noise schematic and data. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions

C.K. and M.K. contributed equally to this work. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS T.D. thanks IISc startup grant for financial support. A.D. thanks nanomission under Department of Science and Technology, Government of India and IISc startup grant for financial support. The authors acknowledge device fabrication and characterization facilities in CeNSE, IISc, Bangalore and Biswanath Chakraborty for helping to take the Raman spectra.

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REFERENCES

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DOI: 10.1021/acs.nanolett.5b04116 Nano Lett. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.nanolett.5b04116 Nano Lett. XXXX, XXX, XXX−XXX