Letter pubs.acs.org/NanoLett
Examining Graphene Field Effect Sensors for Ferroelectric Thin Film Studies A. Rajapitamahuni,† J. Hoffman,§,∥ C. H. Ahn,§ and X. Hong*,†,‡ †
Department of Physics and Astronomy and ‡Nebraska Center for Materials and Nanoscience, University of Nebraska-Lincoln, Nebraska 68588-0299, United States § Department of Applied Physics, Yale University, New Haven, Connecticut 06520, United States S Supporting Information *
ABSTRACT: We examine a prototype graphene field effect sensor for the study of the dielectric constant, pyroelectric coefficient, and ferroelectric polarization of 100−300 nm epitaxial (Ba,Sr)TiO3 thin films. Ferroelectric switching induces hysteresis in the resistivity and carrier density of n-layer graphene (n = 1−5) below 100 K, which competes with an antihysteresis behavior activated by the combined effects of electric field and temperature. We also discuss how the polarization asymmetry and interface charge dynamics affect the electronic properties of graphene.
KEYWORDS: Graphene, ferroelectrics, pyroelectric, sensor, hysteresis, interface
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properties of graphene make it easy to integrate with ferroelectric thin films.7−12,20 By investigating the gating control of the carrier density, one can extract critical parameters of the ferroelectric gate, including the pyroelectric coefficient, dielectric constant, ferroelectric polarization, and Curie temperature. Graphene field effect devices can thus be a sensitive tool to probe the finite size effects in ferroelectric thin films with thickness approaching the fundamental scaling limit of ferroelectric instability. It can also be used to study a range of technologically important phenomena such as pyroelectricity,21 piezoelectricity,22 and flexoelectricity23 at the nanoscale, where surface polarization charge is a critical parameter. In this study, we examine a prototype graphene field effect sensor for the study of ferroelectric thin films. Few layer graphene devices have been fabricated on ferroelectric Ba1‑xSrxTiO3 (BSTO with nominal composition of x = 0.4) thin films, and their pyroelectric, dielectric, and ferroelectric properties have been investigated. Transport properties of graphene point to strong asymmetry in the two polarization states of the BSTO films. We also observe a crossover from ferroelectric switching induced hysteresis in the resistance and carrier density at low temperature to antihysteresis above 100 K, which is attributed to the dynamic response of interface screening charges that are activated by the combined effects of
ith recent advances in large scale production of high quality graphene1,2 and the observation of enhanced functionality of graphene via interfacing with various dielectric materials,3−14 it is of intense technological interest to examine the application prospects of graphene-dielectric hybrid devices. Integrating graphene with complex oxides allows one to implement the rich electronic, magnetic and optical properties of oxide materials into graphene-based nanoelectronics such as high frequency analog devices3,6,11 and nonvolatile memories.7−12 One promising application is to use graphene field effect devices as sensors to study ferroelectric thin films. Ferroelectric materials have a built-in polarization that is switchable and varies with temperature. Traditional methods for characterizing ferroelectrics involve electrical measurements of the change of the surface polarization charge density using a capacitor-geometry, such as the Sawyer−Tower measurements.15 However, direct electric characterization becomes challenging in epitaxial ferroelectric thin films with thickness on the order of a few unit cells, where effects such as the depolarization field significantly modify the ferroelectric ground state.15,16 As a result, most studies on such finite size effects have focused on indirect structural characterizations16,17 or surface studies of their electronic states.18,19 Because of the low density of states and atomic thickness, the electronic properties of few layer graphene (FLG) are highly sensitive to its dielectric environment. Using the Hall effect, one can accurately determine the carrier density, which can be used to extract the surface polarization change of a dielectric gate with high precision. In addition, the flexible mechanical © XXXX American Chemical Society
Received: June 17, 2013 Revised: August 2, 2013
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electric field and temperature. Our work reveals the complicated interplay between ferroelectric polarization and surface charge dynamics, which plays a critical role in the performance of graphene-functional oxide hybrid devices. We have worked with 100−300 nm BSTO films epitaxially grown on (001) Nb-doped SrTiO3 substrates via off-axis radio frequency magnetron sputtering. These BSTO films are predominantly (001)-oriented with surface roughness of ∼0.5 nm (see Figure S1 in the Supporting Information), and the Curie temperature TC is above room temperature as verified by piezo-response force microscopy. The coercive field for these films is 2−3 V/100 nm. We mechanically exfoliate graphite flakes (Sigma-Aldrich) on the BSTO films and identify the thinner graphene flakes optically. The layer number of the nlayer graphene (nLG with n = 1−5) is determined via Raman spectroscopy (Figure 1a) and atomic force microscopy height
Figure 2. Characterization of BSTO thin films using graphene field effect sensors. (a) Pyroelectric effect induced doping level change in graphene at Vg = 0 relative to 300 K for the 100 nm (solid symbol) and 300 nm (open symbol) BSTO films in the as-grown state (square), and polarization up (circle) and down (triangle) states. (b) Dielectric constant vs T for the 100 nm (solid) and 300 nm BSTO films (open). Inset: n vs Vg at 5 K for a 1LG on a 300 nm BSTO film.
At 300 K, the rate of |dP/dT| corresponds to a pyroelectric coefficient of −19 nC/cm2·K, similar to the reported values for BSTO thin films.21,24 |dP/dT| gradually decreases as the sample is cooled below 150 K, and the polarization change saturates around 100 K to ∼3 μC/cm2. A similar temperature dependence is observed on the 300 nm BSTO, which shows a pyroelectric coefficient of −24 nC/cm2K at 300 K. We then pole the 100 nm film to the polarization up Pup (down Pdown) direction by applying a back gate voltage of +9 V (−9 V) at 10 K. It is interesting to note that while the film exhibits a similar P(T) as in the as-grown state for the Pup direction with a pyroelectric coefficient of −20 nC/cm2·K, a much weaker temperature dependence is observed in the polarization for the Pdown state, corresponding to a pyroelectric coefficient of −8.9 nC/cm2·K at 300 K and a total polarization change of ∼1 μC/ cm2. The strong asymmetry between the two polarization states has been widely observed in epitaxial ferroelectric thin films, which can be due to the built-in band bias at the BSTO/STO interface imposed on the two polarization states.16,25 To investigate the dielectric properties of BSTO, we pole the films to the Pup state and work with a voltage range below the coercive voltage. From the gating efficiency we extract the dielectric constant εr = [(ed)/(ε0)][(dn)/(dVg)], where d is the film thickness. Figure 2b inset shows the gate modulation of carrier density at 5 K in a 1LG on 300 nm BSTO, which yields a dielectric constant of 126 ± 7. This value gradually increases to 220 ± 20 at 40 K. From 40 to 250 K, εr exhibits very weak temperature dependence (Figure 2b). A similar temperature dependence has been observed on the 100 nm BSTO film and the value is comparable with what is previously reported on BSTO thin films.24,26 As Vg exceeds the coercive voltage, hysteresis starts to develop in both resistance and carrier density. In Figure 3a, the FLG device is first poled in the Pup state at 10 K by a gate voltage of 9 V, and the polarization field dopes graphene with electrons. As Vg decreases, the doping level decreases and resistance peaks at Vp(Pup) = −0.3 V. The gate voltage is swept back to the positive direction after Vg reaches −3.5 V, and a positive shift of 2.1 V is observed in the resistance peak voltage ΔVp = Vp (Pdown) − Vp (Pup). The direction of the hysteresis agrees with what is expected from ferroelectric switching. When the gating range is extended to −5 V (Figure 3b), ΔVp increases to 3.6 V. Applying larger negative voltage does not
Figure 1. Characterization of graphene on BSTO. (a) Raman spectra of a FLG (n = 4 ± 1) and a 1LG on BSTO substrates normalized to the G peak intensity. The small broad peaks around 1290 and 1615 cm−1 are from the BSTO substrate. (b) Device schematics. (c) Optical image of a 1LG device on 300 nm BSTO. (d) ρ(B) at 2 K taken on the device shown in (c) exhibits SdHO in the Pup state.
measurements. We then fabricate them into Hall bar devices (Figure 1b,c) using e-beam lithography followed by evaporation of 5 nm Cr/30 nm Au as contacts for transport measurements. The conducting Nb:SrTiO3 substrates are used as the back gate electrodes. The resistance and Hall effect measurements have been carried out in a Quantum Design PPMS with 1.8 K base temperature and 9 T magnet. We use standard lock-in techniques with excitation current of 50−200 nA to measure resistance. The transport results reported here are based on two 1LG devices fabricated on a 300 nm BSTO film and one FLG (n = 5±1) device fabricated on a 100 nm BSTO film. At low temperatures, the 1LG samples have field effect mobility of 8400 cm2/(V s) and 10 000 cm2/(V s), respectively, and exhibit Shubnikov de Haas oscillations (SdHO) and quantum Hall effect in magnetic field (Figures 1d and 4) in the polarization up Pup state. We first examine the carrier density n in graphene at zero gate bias (Vg = 0 V) from low field Hall resistance RH = 1/ne. The temperature dependence of n is induced by the pyroelectric change in the polarization field of BSTO. Figure 2a shows the polarization change relative to 300 K as a function of temperature extracted from the doping level of graphene. All measurements are taken as the system warms up. For the 100 nm BSTO film in the as-grown state, the polarization P shows a sharp increase as the temperature decreases from 300 to 150 K. B
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Figure 3. Hysteresis and antihysteresis behaviors observed in BSTO-gated graphene. (a−c) ρ vs Vg for a FLG on 100 nm BSTO at 10 K with different gate voltage ranges. The black and red arrows mark the direction of gate sweep. Also shown in (c) is 1/RH vs Vg at 10 K. The blue arrows indicate where the Hall signal deviates from the single carrier behavior. (d−f) ρ vs Vg for a 1LG on 300 nm BSTO at 2, 100, and 250 K. The black and red arrows mark the direction of gate sweep. (e) Inset: the onset voltage of antihysteresis as a function of temperature for the Pup and Pdown states.
further increase ΔVp (Figure 3c), suggesting the polarization is fully switched. This hysteresis is nonvolatile and reversible, and it is also observed in the Vg-dependence of the carrier density (Figure 3c). From the hysteresis of the carrier density, we extract the remnant polarization (|Pup| + |Pdown|)/2 to be ∼5 μC/cm2, comparable with previously reported values.21 In the fully polarized Pup state (Figure 3b,c), we observe clear kinks in ρ(Vg), or sharp changes in dρ/dVg, at Vg −Vp(Pup) = −0.4 V on the hole-doped side and 0.7 V, 2.6 V on the electron-doped side. As the FLG is a semimetal with band overlap on the order of ∼30 meV,27 the kinks at the lower Vgs correspond to where the Fermi level crosses the band edges of the band overlap regime.7 The band crossing behavior is also manifest in the Hall data, where the RH starts to deviate from the linear Vg-dependence expected for the single carrier behavior due to the existence of compensating electrons and holes (Figure 3c).7,28 The feature at the higher electron density is likely related to the abrupt change of the density of states due to the filling of a higher energy electron band, as observed previously in bilayer graphene gated by an electrolyte.29 The low and high electron density kinks disappear above ∼40 and 100 K, respectively (see Figure S2 in the Supporting Information). We also note that ρ(Vg) in the Pdown state in Figure 3a is broad with the kinks less pronounced than in Figure 3b,c. This is because the polarization is not completely switched at Vg = −3.5 V, and the coexisting Pup and Pdown
domains in the ferroelectric substrate can lead to charge inhomogeneity in graphene, smearing out the features due to band crossing. After sweeping Vg in the negative direction at Vg < −4 V, a small resistance hysteresis starts to develop in the opposite direction compared to the ferroelectric switching. This antihysteresis occurs at progressively lower gate voltage at higher temperatures. As shown in Figure 3d−f, the competition between the ferroelectric hysteresis and antihysteresis yields a lower ΔVp in graphene with increasing temperature. At 80−100 K, they fully compensate each other, resulting in no net shift of ΔVp. Increasing the temperature further leads to antihysteresis dominated switching. Such crossover from ferroelectric hysteresis to antihysteresis is observed on all devices fabricated on the 100 and 300 nm BSTO films. The onset of the antihysteresis state is signaled by a sudden saturation in both resistivity (see Figure S3 in the Supporting Information) and carrier density, indicating that an additional mechanism has been activated to screen the polarization change in the ferroelectric gate, which prevents graphene from sensing the field effect modulation. As shown in the inset of Figure 3e, the onset voltage Vonset decreases with increasing temperature for both polarization directions, further confirming that the screening is activated by the combined effects of thermal excitation and electric field. It is worth mentioning that the crossover temperature coincides with where the ferroelectric C
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polarization is fully developed and the pyroelectric effect saturates (Figure 2a). Similar antihysteresis behavior has been previously observed in carbon nanotube and graphene field effect devices gated by both ferroelectrics and conventional dielectrics such as SiO2 and has been attributed to either the dynamic screening of interface adsorbates9,30,31 or charge injection into the interface defect states.32 Our BSTO films have TCs above room temperature, and the out-of-plane polarization field is screened by charged adsorbates or surface states in the ambient conditions before the graphene flakes were exfoliated.9 Activated by temperature, such an interfacial charge layer can respond dynamically to the polarization change induced by the gate voltage, which shunts the field effect modulation of graphene. This scenario can naturally explain the different switching results previously observed in graphene−ferroelectric hybrid devices. For example, in graphene gated by epitaxial Pb(Zr,Ti)O3 substrates, both hysteresis and antihysteresis behaviors have been observed depending on the crystallinity of the substrate, the deposition temperature of graphene, and the sweeping rate and range of Vg.9,10,12,20 On the other hand, ferroelectric hysteresis dominated switching is observed in samples with a ferroelectric top-gate geometry,8 where an interfacial screening charge layer is not present at the time the top gate is deposited. In our experiments, the low-temperature remnant polarization of the BSTO films is ∼5 μC/cm2, and we deduce from the pyroelectric change the room-temperature polarization to be ∼2 μC/cm2. The interfacial charge layer accumulated in the ambient conditions is thus not sufficient to completely compensate the fully developed polarization below 100 K. As a result, we observe antihysteresis dominated by dynamic interfacial charge screening at high temperature, crossing over to ferroelectric switching dominated behavior below 100 K. The strong asymmetry in the two polarization states is also manifest in the transport properties of graphene. As shown in Figure 3d−f, the hysteresis branch for the 1LG corresponding to Pdown is more conductive than the Pup branch, especially at high temperatures. This can be due to either higher mobility or the presence of charge inhomogeneity. To identify the origin of this asymmetric behavior, we have studied the transport of graphene in magnetic field. At high magnetic field, clear SdHOs are observed in ρ(B) for the Pup state (Figure 1d). At 9 T, we observe well-developed quantum Hall states at filling factors of ν = 4l + 2 in ρxx(Vg) (Figure 4a) and ρxy(Vg) (Figure 4b), where l is an integer. On the other hand, in the Pdown branch these features are smeared out despite the higher conductivity, clearly signaling that the carrier density is not homogeneous in this state. This is consistent with the observation in the FLG device fabricated on 100 nm BSTO (Figure 3b,c), where for ρ(Vg) in the Pdown state the features corresponding to band crossing are not as clearly present compared with that in the Pup state. Two scenarios can contribute to the charge inhomogeneity in graphene. The first is associated with the built-in polarization asymmetry of BSTO thin films. Domain structures with mixed polarization directions may be promoted by an applied field even below the coercive field when the film is poled in the energetically unfavorable state,16,25 which can result in charge density variation in graphene over a range of Vg close to the ferroelectric switching voltage. The second possibility is that the redistribution of screening charges during polarization switching can lead to incomplete screening in different regions of the sample. As shown in the inset of Figure
Figure 4. Quantum Hall effect observed in BSTO-gated graphene. (a) ρxx and (b) ρxy vs Vg for a 1LG at 2 K and 9 T. The horizontal bars in (b) mark the quantized plateaux for the labeled filling factors in 1LG. The black and red arrows indicate the direction of gate sweep.
3e, the activation voltage for interface screening in the Pup state is lower compared with the Pdown state at the same temperature, reflecting lower excitation energy. This means different screening mechanisms or interfacial charge types are involved in screening different polarization directions. Possible candidates include interface adsorbates such as water molecules, H+, OH− groups, and O2,9,17,19,30,31 and ferroelectric surface defect states and mobile ions.32−34 The specific distribution of the interface charge layer may affect strongly the screening field strength. We also note that when the gate sweep range exceeds Vonset, the antihysteresis behavior causes small shift in the resistance hysteresis in different gate sweeps, which can be due to the variation in the distribution of the activated interfacial screening charges. Further experiments with controlled graphene−ferroelectric interface conditions are required to identify the dominant screening mechanism/charge type for the two polarization directions. The interfacial screening charges can modify the disorder energy landscape, which is further affected by the high-k dielectric environment. From the Dingle plot of the oscillation amplitude in the SdHO shown in Figure 1d,35 we extract the quantum scattering time τq = 59 fs at n = 7.28 × 1012/cm2. This carrier density corresponds to a gate voltage of >100 V for a 300 nm SiO2 substrate. The Hall mobility μHall at this density is 8000 cm2/(V s), yielding a transport scattering time τt = m*μHall/e of 250 fs. Here m* is the effective mass of electron at this density. The high ratio of τt/τq = 4.2 between the transport and quantum scattering times suggests that the sample is dominated by small angle scattering due to long-ranged scatterers.36 We expect that the interface screening charge D
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(6) Lin, Y.-M.; Dimitrakopoulos, C.; Jenkins, K. A.; Farmer, D. B.; Chiu, H.-Y.; Grill, A.; Avouris, P. Science 2010, 327, 662. (7) Hong, X.; Posadas, A.; Zou, K.; Ahn, C. H.; Zhu, J. Phys. Rev. Lett. 2009, 102 (13), 136808. (8) Zheng, Y.; Ni, G.-X.; Toh, C.-T.; Zeng, M.-G.; Chen, S.-T.; Yao, K.; Ozyilmaz, B. Appl. Phys. Lett. 2009, 94, 163505. (9) Hong, X.; Hoffman, J.; Posadas, A.; Zou, K.; Ahn, C. H.; Zhu, J. Appl. Phys. Lett. 2010, 97 (3), 033114. (10) Zheng, Y.; Ni, G. X.; Bae, S.; Cong, C. X.; Kahya, O.; Toh, C. T.; Kim, H. R.; Im, D.; Yu, T.; Ahn, J. H.; Hong, B. H.; Ozyilmaz, B. EPL 2011, 93 (1), 17002. (11) Hong, X.; Zou, K.; DaSilva, A. M.; Ahn, C. H.; Zhu, J. Solid State Commun. 2012, 152 (15), 1365−1374. (12) Baeumer, C.; Rogers, S. P.; Xu, R. J.; Martin, L. W.; Shim, M. Nano Lett. 2013, 13 (4), 1693−1698. (13) Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.; Hone, J. Nat. Nanotechnol. 2011, 5 (10), 722−726. (14) Standley, B.; Mendez, A.; Schmidgall, E.; Bockrath, M. Nano Lett. 2012, 12 (3), 1165−1169. (15) Rabe, K. A.; Dawber, M.; Lichtensteiger, C.; Ahn, C. H.; Triscone, J. M., Modern physics of ferroelectrics: Essential background. In Physics of Ferroelectrics: A Modern Perspective; Rabe, K. M., Ahn, C. H., Triscone, J. M., Eds.; Springer-Verlag: Berlin, 2007; Vol. 105, pp 1−30. (16) Lichtensteiger, C.; Dawber, M.; Triscone, J. M. Physics of Ferroelectrics: A Modern Perspective; Springer: New York, 2007; Vol. 105; pp 305−337. (17) Fong, D. D.; Kolpak, A. M.; Eastman, J. A.; Streiffer, S. K.; Fuoss, P. H.; Stephenson, G. B.; Thompson, C.; Kim, D. M.; Choi, K. J.; Eom, C. B.; Grinberg, I.; Rappe, A. M. Phys. Rev. Lett. 2006, 96 (12), 127601. (18) Shin, J.; Nascimento, V. B.; Borisevich, A. Y.; Plummer, E. W.; Kalinin, S. V.; Baddorf, A. P. Phys. Rev. B 2008, 77, 24. (19) Shin, J.; Nascimento, V. B.; Geneste, G.; Rundgren, J.; Plummer, E. W.; Dkhil, B.; Kalinin, S. V.; Baddorf, A. P. Nano Lett. 2009, 9 (11), 3720−3725. (20) Yusuf, M. H.; Nielsen, B.; Dawber, M.; Du, X. Unpublished work, 2013. (21) Sharma, A.; Ban, Z. G.; Alpay, S. P.; Mantese, J. V. J. Appl. Phys. 2004, 95 (7), 3618−3625. (22) Baek, S. H.; Park, J.; Kim, D. M.; Aksyuk, V. A.; Das, R. R.; Bu, S. D.; Felker, D. A.; Lettieri, J.; Vaithyanathan, V.; Bharadwaja, S. S. N.; Bassiri-Gharb, N.; Chen, Y. B.; Sun, H. P.; Folkman, C. M.; Jang, H. W.; Kreft, D. J.; Streiffer, S. K.; Ramesh, R.; Pan, X. Q.; TrolierMcKinstry, S.; Schlom, D. G.; Rzchowski, M. S.; Blick, R. H.; Eom, C. B. Science 2011, 334 (6058), 958−961. (23) Lu, H.; Bark, C. W.; de los Ojos, D. E.; Alcala, J.; Eom, C. B.; Catalan, G.; Gruverman, A. Science 2012, 336 (6077), 59−61. (24) Lee, J. S.; Park, J. S.; Kim, J. S.; Lee, J. H.; Lee, Y. H.; Hahn, S. R. Jpn. J. Appl. Phys., Part 2 1999, 38 (5B), L574−L576. (25) Lichtensteiger, C.; Dawber, M.; Stucki, N.; Triscone, J. M.; Hoffman, J.; Yau, J. B.; Ahn, C. H.; Despont, L.; Aebi, P. Appl. Phys. Lett. 2007, 90 (5), 052907. (26) Shaw, T. M.; Suo, Z.; Huang, M.; Liniger, E.; Laibowitz, R. B.; Baniecki, J. D. Appl. Phys. Lett. 1999, 75 (14), 2129−2131. (27) Partoens, B.; Peeters, F. M. Phys. Rev. B 2006, 74 (7), 075404. (28) Zhu, W. J.; Perebeinos, V.; Freitag, M.; Avouris, P. Phys. Rev. B 2009, 80 (23), 235402. (29) Efetov, D. K.; Maher, P.; Glinskis, S.; Kim, P. Phys. Rev. B 2011, 84 (16), 161412. (30) Kim, W.; Javey, A.; Vermesh, O.; Wang, O.; Li, Y. M.; Dai, H. J. Nano Lett. 2003, 3 (2), 193−198. (31) Lee, J. S.; Ryu, S.; Yoo, K.; Choi, I. S.; Yun, W. S.; Kim, J. J. Phys. Chem. C 2007, 111 (34), 12504−12507. (32) Paruch, P.; Posadas, A.-B.; Dawber, M.; Ahn, C. H.; McEuen, P. L. Appl. Phys. Lett. 2008, 93 (13), 132901. (33) Wang, H. M.; Wu, Y. H.; Cong, C. X.; Shang, J. Z.; Yu, T. ACS Nano 2010, 4 (12), 7221−7228.
layer gives rise to a high density of charged impurities and affects the mobility of graphene. The high τt/τq results from the high dielectric constant of the BSTO substrate, which provides more effective dielectric scattering of the charged impurities.35,36 In conclusion, we have demonstrated the working principle of graphene field effect sensors for the study of the pyroelectric, dielectric, and ferroelectric properties of ferroelectric thin films. In graphene/BSTO hybrid devices, we observe ferroelectric hysteresis in resistance and carrier density below 100 K, which crossovers to an antihysteresis behavior activated by the combined effects of electric field and temperature. Our work reveals the critical role played by the interface chemistry in the performance of graphene−ferroelectric oxide hybrid devices.
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ASSOCIATED CONTENT
S Supporting Information *
Structural and surface characterizations of Ba1−xSrxTiO3 thin films; temperature dependence of ρ(Vg) in few layer graphene; onset voltage in resistivity antihysteresis. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Present Address ∥
(J.H.) Materials Science Division, Argonne National Laboratory. Author Contributions
(Ba,Sr)TiO3 samples were grown at Yale University. Graphene device fabrication and transport measurements were carried out at the University of Nebraska-Lincoln. The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank J. Zhu and K. Zou for helpful discussions, J. Gardner, J. Ngai, V. Singh, T. Vo, and Z. Xiao for technical assistance, and Y.F. Lu and A. Sinitskii for providing access to their Raman facilities. This work is supported by NSF Grants CAREER DMR-1148783 and MRSEC DMR-0820521, and Nebraska Research Council. C.H.A. acknowledges support from NSF Grant DMR 1119826.
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ABBREVIATIONS STO, SrTiO3; BSTO, (Ba,Sr)TiO3; nLG, n-layer graphene; FLG, few layer graphene REFERENCES
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