Characterizing intrinsic charges in top gated bilayer graphene device by Raman spectroscopy

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Characterizing intrinsic charges in top gated bilayer graphene device by Raman spectroscopy D.L. Mafra a,1, P. Gava b,1, L.M. Malard a, R.S. Borges c, G.G. Silva c, J.A. Leon a, F. Plentz a, F. Mauri b, M.A. Pimenta a,* a b c

Departamento de Fı´sica, Universidade Federal de Minas Gerais, 30123-970 Belo Horizonte, Brazil IMPMC, Universite´ Paris 6 et 7, CNRS, IPGP, Paris, France Departamento de Quı´mica, Universidade Federal de Minas Gerais, 30123-970 Belo Horizonte, Brazil

A R T I C L E I N F O

A B S T R A C T

Article history:

In this work we study the behavior of the optical phonon modes in bilayer graphene devices

Received 25 October 2011

by applying top gate voltage, using Raman scattering. We observe the splitting of the

Accepted 4 March 2012

Raman G band as we tune the Fermi level of the sample, which is explained in terms of

Available online 10 March 2012

mixing of the Raman (Eg) and infrared (Eu) phonon modes, due to different doping in the two layers. We theoretically analyze our data in terms of the bilayer graphene phonon self-energy which includes non-homogeneous charge carrier doping between the graphene layers. We show that the comparison between the experiment and theoretical model not only gives information about the total charge concentration in the bilayer graphene device, but also allows to separately quantify the amount of unintentional charge coming from the top and the bottom of the system, and therefore to characterize the intrinsic charges of bilayer graphene with its surrounding environment.  2012 Elsevier Ltd. All rights reserved.

1.

Introduction

Bilayer graphene has attracted a lot of attention recently because of its special low energy electronic dispersion, in which a tunable band gap can be opened by application of a transverse electric field [1–8]. Such device is desirable for low energy photo-emitters and detectors possessing a high tunability by the control of charge concentrations on the graphene layers. Recent experimental demonstration of this tunable band gap in bilayer graphene was based on the absorption measurements in the infrared region [6–8] or by electric transport measurements [4,5]. However the tunable band gap bilayer graphene device operation can be greatly influenced by the surrounding environment. Typically, unintentional doping charges coming from the top and the bottom of the system can accumulate on bilayer

graphene, giving rise to an unintentional electric field which determines a non-homogeneous doping between the layers and the opening of a band gap in the band structure, without any applied electric field [9]. In this work we use Raman spectroscopy to monitor the unintentional charge coming from the top and the bottom of the system, which gives information on the electrostatic environment of the sample and which helps to characterize the bilayer devices for further applications. The band gap opening and tunability in bilayer graphene is based on the application of an electric field E perpendicular to the layers, given by: E ¼ ðntop þ nbot Þjej=ð20 Þ

ð1Þ

where ntop and nbot are the charge carriers coming from the top and the bottom of bilayer graphene, respectively, 0 is

* Corresponding author. E-mail address: [email protected] (M.A. Pimenta). 1 D.L. Mafra and P. Gava contributed equally for the paper. 0008-6223/$ - see front matter  2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.carbon.2012.03.006

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the vacuum permittivity, and e is the electronic charge. Raman spectroscopy has already shown to be a fast and non-destructive tool to characterize graphene samples [10,11] and doping effects [12–16], however no carefully analysis has been done to demonstrate the effect of non-homogeneous doping in bilayer graphene devices. Recent theoretical calculations made by Gava et al. [9] suggest that from the analysis of the Raman spectra of gated bilayer graphene it is possible to quantitatively identify the amount of non-intentional charges coming from the atmosphere and from the substrate and to characterize the electrostatic environment of few-layers graphene. In this work we study the dependence of the G band of bilayer graphene on the gate voltage. From the direct comparison between the experimental and the theoretically simulated Raman spectra, and from the analysis of the positions, full width at half maximum (FWHM) and relative intensities of the two Raman peaks as a function of the electron concentration, we were able to estimate the charge unintentionally accumulated on the device from the environment.

2.

Experimental details

Fig. 1(a) shows the bilayer-graphene field-effect transistor (FET) used in the experiment. Graphene samples were produced by micro-mechanical cleavage of graphite and deposited on Si covered with 300 nm of SiO2. Top gating was achieved by using a polymer electrolyte consisting of polyethylene glycol (PEG) and NaClO4 with ratio concentration of 1:0.25, and the gate voltage was applied between a gold electrode in contact with the graphene layer and a platinum wire electrode inserted in the electrolyte (see the schematic setup in Fig. 1(b)). The contacts were made by optical lithography. The Raman measurements were done in the back scattering configuration at room temperature using a triple monochromator spectrometer (DILOR XY) using 2.41 eV as excitation laser energy. The spot size of the laser was 1 lm using a 80· objective and the laser power was kept at 1.4 mW.

3.

Results and discussion

The interface between graphene and polymer electrolyte has been shown experimentally to behave like a double layer capacitor of thickness in the order of nanometers [17]. Therefore, the geometric capacitance of the electrolyte is very high compared to bottom gate devices where the thickness of the dielectric material is much larger (typically 300 nm).

Capacitance measurements of the polymeric electrolyte used in the experiment were performed by Impedance Spectroscopy with frequency analyzer AUTOLAB PGSTAT30 by using a symmetrical cell with two Au electrodes and a polymer electrolyte layer. The impedance (Z) measurements for the electrolytes were carried out with frequency ranging from 50 kHz to 0.5 Hz at 0 V with 10 mV amplitude. The expression Z = 1/ixC, where x is the frequency, was used to determine the capacitance (C) and the value obtained for capacitance per unit area for the interface electrolyte/bilayer was 1.5 · 106 F cm2. However, the shape and the thickness of the dielectric double layer depend on the specific surface at contact with the electrolyte. Therefore, from the measured value of impedance, we can only have the order of magnitude of the geometric capacitance CG of the electrolyte in contact with bilayer graphene. In the case of bilayer graphene with Bernal AB layer stacking, both the electronic and phonon bands split into two energy sub-bands with special symmetries [18]. The E2g phonon mode of monolayer graphene splits into two distinct modes, associated with the symmetric (S) and anti-symmetric (AS) displacements of the atoms in the two layers with respect to inversion symmetry [19]. The S and AS modes belong to the two double degenerated representation Eg and Eu of the D3d point group, respectively [9,19–21]. The Eu mode is not Raman active and, therefore, the G band of isolated bilayer graphene is composed of only one peak. However, when the two layers of bilayer graphene have different charge carrier concentration, induced by the application of an external gate voltage, the inversion symmetry of bilayer graphene is broken, lowering the symmetry of the system. As a consequence of the induced asymmetry between the two layers, the two S and AS modes are mixed each other, the two new eigenmodes have the Raman active S component, and therefore two peaks are observed in the G band of bilayer graphene [9,19–21]. In Fig. 2(a) (red dashed curves) we show the experimental Raman spectra taken with the application of top gate voltage (Vg) from 1.50 to 1.00 V. The G band splitting into two components Gh and Gl (higher and lower frequency peak, respectively) can be clearly observed for Vg below 0.6 V. In this work we compare our experimental spectra with theoretical calculations from Ref. [9]. In particular, in Ref. [9] the authors considered the C phonon self-energy in order to compute the electron–phonon coupling contribution to the variation of the frequency, broadening, and relative Raman intensity of the two phonon modes in bilayer graphene, as a function

Fig. 1 – (a) Optical microscope image of the graphene sample before application of the polymer electrolyte. (b) Schematic illustration of the device and the experimental setup.

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Fig. 2 – (a) Comparison between experimental (red dashed line) and theoretical (black continuous line) spectra for different Vg as obtained from the direct fit of spectra; (b–d) Frequency xh/l, FWHM Ch/l and ratio of Ih/l as obtained fitting the experimental spectra with two Lorentzians and compared with theory. The dots are the experimental data and the full curves are the theoretical calculations from Ref. [9]. The blue dashed line corresponds to the values of n to which we expect a jump in the quantum capacitance. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

of the electron concentration n and as a function of the induced charge from the bottom of the system, nbot. The phonon self-energy and the band structure of gated bilayer graphene are computed using a tight-binding scheme as described in details in Ref. [9]. In order to compare the experimental spectra and theoretical calculations, we need to convert Vg into electron concentration n using the expression bVg ¼ ðn  n0 Þe;

ð2Þ

where e is the electronic charge (e = |e|). In the comparison the total capacitance b, which includes the quantum capacitance (CQ) and geometrical capacitance (CG) [14], and the intrinsic doping at the zero gate n0 are used as fitting parameters. Moreover, by the comparison between experimental and theoretical results from Ref. [9] we can estimate the charges unintentionally adsorbed, at zero gate, from the top and bottom of the device, n0top and n0bot respectively. These quantities are related to n0 by n0 ¼ n0top þ n0bot, and therefore we only used n0bot as additional fitting parameter. n0bot and n0 are the two independent fitting parameters characterizing

the charge transfer on the system. Finally, the theoretical FWHM Cth calculated as a function of n and n0bot is given by electron–phonon and an-harmonic phonon–phonon interaction [9]. Therefore, in order to take into account other factors determining a finite lifetime and neglected in the calculations, we used in the fitting procedure a parameter C0, independent on the total charge n and equal for the two peaks, related to the total FWHM by C = Cth + C0. In Fig. 2(a) we show the comparison between the experimental spectra (red dashed curve) and the theoretical one (black continuous curve). For each Vg the theoretical spectra is obtained as the sum of two Lorentzians, Lh (x) for the Gh peak and Ll (x) for the Gl peak. The two Lorentzians are centered in xh/l, with FWHMs Ch/l = Cthh/l + C0, and with area Ih/l, as follows: Lh=l ðxÞ ¼ Ih=l ðCh=l =2Þ=½ðx  xh=l Þ2 þ ðCh=l =2Þ2 :

ð3Þ

xh/l, Cthh/l, and Ih/l are evaluated according with the theory from Ref. [9] where they are calculated as a function of n and n0bot. In order to convert n and n0bot into Vg we used Eq. (2).

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In particular, we used two different parameters, b+and b, for positive and negative Vg, which induce positive and negative n (i.e., electron and hole doping charge), respectively. The fit is performed computing the v2, i.e., the square of the difference between the experimental and theoretical spectra, averaged over all the measured Raman range and over different Vg. We considered Vg in the range of ±0.5 V. This choice is motivated by the fact that for large values of Vg the linear relation between gate voltage and charge could be modified, and charges from the electrolyte could accumulate on the bottom of the sample, making the fit results less reliable. The values for the parameters used in the fit (i.e., b+, b, n0, n0bot , and C0) are varied in uniform and dense grids. In Fig. 2(a) we show the best fit obtained with b+ = (3.70 ± 0.15) · 106 F cm2 and b = (4.60 ± 0.15) · 106 F cm2, n0 = (0.15 ± 0.02) · 1013 cm2, n0bot ¼ ð0:00  0:02Þ  1013 cm2 , and C0=(7.5 ± 0.1) cm1. The error bar for the fitting parameters is estimated as the variation giving a v2 augmentation lower than 1%. For this values found for b, the range of Vg used in the experiment (from 1.6 to 1.0 V) corresponds to a change in the Fermi level position of about 0.51 to 0.38 eV and a change in the charge concentration of about 4.7 · 1013 cm2 to 2.3 · 1013 cm2. Notice that the agreement between the experimental and simulated spectra is excellent in the range 0.5 to 0.5 V. The slight shifts out of this range can be ascribed to a possible hysteresis in the experiment, and to the fact that we did not consider in our model the expected jump of the quantum capacitance (CQ) when, increasing (decreasing) the Fermi level, we reach the second conduction band (penultimate valence band) in bilayer graphene [14]. The Fermi level value to when the second conduction (valence) band starts to be filled (emptied) is ±0.4 eV [22–24]. This corresponds to a charge concentration of about n = ± 3 · 1013 cm2 (see the blue dashed line in Fig. 2(b)–(d)), and according to our values of n0 and b obtained from the fit, the gate values at which the jumping of the quantum capacitance is expected are around Vg = 1.3 V for positive gate voltage and Vg = 1.0 V for negative gate voltage. The different values of b+ and b can be ascribed to the different  mobilities of the positive (Na+) and negative (ClO4 ) ions. 0 The value found for the nbot ¼ 0 shows that the amount of charge transferred from the substrate to the bottom layer of the sample in this case is negligible. On the other hand, the unintentional doping concentration found for the top layer is n0bot ¼ 0:15  1013 cm2 . Although it is known that the polymer electrolyte eliminates hysteresis and diminishes the influence of external effects, such as changes in gas adsorption from ambient [25], the polymer electrolyte layer itself can, for instance, contain residual water or absorb water from the humid air [26], and this will contribute to an unintentional charge transfer, because water can diffuse through the polymer and be adsorbed in the graphene layer. All the G band experimental spectra of Fig. 2(a) were also fitted using two Lorentzians in order to extract the frequencies and full width at half maximum (FWHM) of the two components Gh and Gl, as well as the relative Raman intensity, i.e., the ratio between the Raman intensities of the modes with higher frequency (Ih) and lower frequency (Il). Fig. 2(b) and (c) shows, respectively, the dependence of the Gh (red dots) and Gl (black dots) frequencies and FWHM C as a function

of the electron concentration. The full lines are the theoretical calculations based on Ref. [9]. The dependence of the frequency of the Gh and Gl Raman peaks (Fig. 2(b)) is well described by the calculation of the phonon self energy as a function of charge concentration. The distinct behaviors of the Gh and Gl is qualitatively explained by the different electron–phonon couplings for the symmetric and anti-symmetric phonon modes with inter-band and intra-band electron– hole pairs, as explained in Ref. [19] and Ref. [20]. While Gh blueshifts with charge carrier concentration due to inter-band transitions, the Gl mode redshifts due to intra-band transitions when the Fermi energy is changed. For the FWHM dependence, while Ch does not change with n, the Cl is maximum near n = 0 and minimum for values of n corresponding to values of EF larger than half of the phonon energy, as has been observed before in both mono and bilayer graphene. It is worth to mention that the scattered data points for the frequencies, FHWM and relative intensities shown in Fig 2(b)–(d) are mostly caused by charge carrier fluctuation during the measurement, where a hysteresis of the charge neutrality point is found by sweeping the gate voltage up and down. The shift of the neutrality point can reach 0.25 V in a range of 1 V of gate voltage due to hysteresis effect [27]. In Fig. 2(d) we plot the dependence of the Ih/Il as a function of n. The quantity Ih/Il shows a minimum value between n1 to 1 · 1013 cm2 and increases more strongly for positive carrier concentration. The underestimation of the theoretical results for high negative and positive charge concentrations can be ascribed to the incertitude in the Ih/Il experimental values and the approximations made in the theoretical model.

4.

Conclusion

In summary, a detailed analysis of the G band of top gated bilayer graphene is presented. We observed that, unlike in the unbiased case where the G Raman band is composed by only one peak, the gate voltage breaks the inversion symmetry and the G band splits in two modes, that are combinations of the symmetric and anti-symmetric modes of the unbiased bilayer graphene. We analyze the dependence of the frequency and the relative intensities of the peaks with higher and lower frequency as a function of the electron concentration and we compared the experimental results with theoretical calculations from Ref. [9]. From this comparison, we could estimate the unintentional carrier concentration adsorbed on the device, at zero gate, from the substrate, n0bot , and from the electrolyte, n0top , and we found n0bot = 0.0 and n0top = 0.15 · 1013 cm2, showing that Raman spectroscopy is a powerful technique to study the electrostatic environment of graphene.

Acknowledgements We would like to acknowledge Nacional de Grafite (Brazil) for providing us the graphite samples. D.L.M. and L.M.M. acknowledges the support from the Brazilian Agency CNPq. Calculations were performed at the IDRIS supercomputing center (Projects No. 081202 and No. 081387).

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