Field-Emission Resonances on Graphene on Insulators - The Journal

Article pubs.acs.org/JPCC

Field-Emission Resonances on Graphene on Insulators Paï vi Jar̈ vinen,† Avijit Kumar,† Robert Drost,† Shawulienu Kezilebieke,† Andreas Uppstu,‡ Ari Harju,‡ and Peter Liljeroth*,† †

Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, 00076 Aalto, Finland COMP Centre of Excellence, Department of Applied Physics, Aalto University School of Science, P.O. Box 11100, 00076 Aalto, Finland

Downloaded by EMORY UNIV on August 25, 2015 | http://pubs.acs.org Publication Date (Web): August 20, 2015 | doi: 10.1021/acs.jpcc.5b06374

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ABSTRACT: Field-emission resonances (FERs) can be used to map the work function of a conducting surface with a high spatial resolution. While FERs have been measured on different graphene systems, measurements on graphene transferred on insulating substrates have not been carried out previously. Here we have measured FERs on graphene transferred on hexagonal boron nitride (h-BN) and silicon dioxide (SiO2) substrates. We have also developed a simple 1D model that can be used to directly interpret the constant current spectroscopy experiments. On both surfaces, FERs can be used to map the local work function changes.

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INTRODUCTION When an electron resides outside a surface, it feels the Coulomb potential due to its image charge. This interaction sets up a series of 1D, hydrogen-like bound states called image potential states (IPSs).1 On conductive substrates, these states can be probed by tunneling spectroscopy (e.g., using scanning tunneling microscopy, STM). In a tunnel junction, the electric field across the junction gives rise to a Stark shift, and the resulting states between the tip and the surface are called fieldemission resonances (FERs).2 FERs arise in the Fowler− Nordheim region of tunneling,3 that is, when the applied voltage is higher than the work function of the surface. FERs were first measured in STM in 1985,4 and have, since then, been widely employed by the STM community to measure the local work function of a surface with a high spatial resolution.5 In addition to studying work function variations of nanostructures,6−9 FERs on graphene have been measured on epitaxially grown graphene on different substrates, such as G/SiC,10 G/ Rh(111),11 and G/Ru(0001).12 Additionally, the confinement of FERs in graphene nanoislands on Ir(111) has been measured.13 All of the experimental studies of field-emission resonances have so far been carried on systems where the substrate was a bulk conductor. Concentrating on graphene, in all of the previous examples, the graphene was grown on either a metal or a highly doped semiconductor, which contribute to the effective screening and hence the field-emission resonances. Thus, there is a considerable conceptual interest in studying FERs on a graphene monolayer deposited on an insulating substrate. In addition to the fundamental significance of probing FERs on an atomically thin conductor, graphene on an insulating substrate is also more relevant to device applications. While © XXXX American Chemical Society

epitaxial graphene grown under ultrahigh vacuum (UHV) conditions is an excellent model system to study the fundamental properties of graphene, it has limited significance from an application point of view. Thus, many strategies to transfer chemical vapor deposition (CVD)-grown graphene14 away from metal substrates have been developed.15 In addition to SiO2,16,17 CVD-grown graphene has been transferred on a multitude of substrates, such as h-BN18 and several transitionmetal dichalcogenides;19 however, there are no reports on FERs on graphene on insulators. In contrast with epitaxial graphene systems, measuring FERs on graphene transferred on insulators is a more direct test of screening in graphene. Here we present first experimental results on image potential states on an atomically thin conductor by studying FERs on graphene on h-BN and SiO2 substrates via low-temperature STM and scanning tunneling spectroscopy. The results differ qualitatively from earlier experiments on epitaxial graphene on SiC, where Fabry−Perot-type resonances were observed.10 We interpret our results in terms of an effective 1D model, which explicitly considers current transport through the image potential states. These experiments demonstrate the feasibility of observing FERs on graphene and using them as a probe of the local work function in graphene devices at extremely high spatial resolution.

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EXPERIMENTAL METHODS In this work, graphene was grown via chemical vapor deposition (CVD) on Cu foils (Alfa Aesar, 99.999%) and transferred via the method described in ref 14. Raman Received: July 3, 2015

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DOI: 10.1021/acs.jpcc.5b06374 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

On G/SiO2, we also observe one resonance at low bias (2.7 V see inset, Figure 1c). Surprisingly, the first resonance in the n-series is split into two distinct components, one at 3.9 V and the other at 4.6 V. The relative intensity of each component varies between different measurement spots on the sample. In addition, there are regions of the G/SiO2 sample where FERs are not observed (see below); however, all of the observed firstorder resonance peaks on G/SiO2 were split into two components. A partial splitting of the first resonance have been observed, for example, on h-BN/Ir(111)9 and G/ Ir(111),13 due to moiré-induced local work function modulations. Even though the splitting on G/SiO2 is very large (ca. 0.7 eV), it might be due to local inhomogeneities in graphene. For instance, it is reasonable to expect that a hydration layer as well as other impurities exist at the G/SiO2 interface as a remnant of the transfer process,17 whereas the G/h-BN interface is known to be self-cleaning.26 Also, G/SiO2 has been suggested to be partially suspended which might contribute to the observed response.27,28 If the spatial resolution of the measurement is not sufficient to resolve the scale of the inhomogeneities, apparent splitting of the first resonance would result. STM in the field-emission resonance regime is not expected to have atomic resolution; the effective tunneling area is likely to be up to a couple of nm2. We have analyzed the system in terms of an effective 1D model (Figure 2). Typically, the modeling of FERs involves

spectroscopy was used to check the quality of graphene and to verify that monolayer graphene was produced. h-BN flakes were exfoliated onto Si/SiO2 substrates (285 nm thermal oxide); subsequently, graphene was transferred onto these samples. This way, measurements on G/h-BN and G/SiO2 could be done on the same sample.20 The substrates with a transferred graphene layer were inserted into a UHV system (base pressure ∼10−10 mbar) and annealed gently to remove adsorbed impurities. A Createc LT-STM and a Unisoku LT-STM were used for imaging and spectroscopy. All of the measurements were carried out in UHV and T = 5 K. STM images were processed with Gwyddion software.21

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RESULTS AND DISCUSSION Figure 1a,b shows STM topographic images on G/h-BN and G/SiO2 surfaces, respectively. Compared with G/SiO2, G/h-

Figure 1. STM topographs of (a) G/h-BN and (b) G/SiO2. The insets show atomic resolution. (c) FERs measured in the constant current mode on G/h-BN and G/SiO2. On G/h-BN, the dI/dV spectrum shows typical features of graphene FER, with the first resonance peak at 4.3 V. The first resonance peak on G/SiO2 is split into two components, one at 3.9 V and the other at 4.6 V. The inset shows zoom-in to the low bias region of the spectra. The scale bars are 3 nm.

BN is much less corrugated, and it shows the characteristic moiré pattern resulting from the lattice mismatch between graphene and the underlying h-BN.22 These observations are in good accordance with previous observations of graphene on hBN and SiO2.18,20,23−25 dI/dV spectra in the constant-current mode up to high biases were measured on both surfaces (Figure 1c). The spectrum of G/h-BN exhibits features typical of FERs on graphene on various substrates. Previous experiments have found two series of resonance peaks, denoted as mand n-series, which have been observed on G/Rh(111)11 and G/Ru(0001).12 The m-series, which appears at low bias voltage, was attributed to resonances where the corresponding wave function had the highest amplitude between graphene and the substrate, and it was not observed on top-region of the graphene moiré.11 On the corrugated graphene moiré on Ru(0001), the top region corresponds to the largest graphene− metal distance. There, the interaction between graphene and the underlying metal is weak and results from essentially pure vdW interaction. On G/h-BN, the only observed resonance in the low-bias regime is at 2.4 V (inset, Figure 1c), and it may also be attributed to variations in the graphene density of states. It did not vary according to the graphene moiré, which is probably related to the very small actual topographic corrugation of graphene on h-BN. The first resonance in the n-series appears at 4.3 V and is followed by a series of higher order resonances.

Figure 2. (a) Model potential used in the FER simulations. The black line describes the potential well created by graphene and the tip. (b) Typical fit of experimental z(V) spectrum (black) and the simulated results (red). The inset shows the measured dI/dV signal, and the vertical lines indicate the simulated peak positions.

solution of the Schrödinger equation in an effective potential, which yields the energies of the image-potential states. In some cases, also the Stark shift due to the electric field set up by the tip−substrate bias is taken into account. In these types of approaches, the comparison with experiment only considers the energies of the FERs. We go a step further by explicitly simulating the actual constant-current STM experiment and comparing the theoretical and experimental z(V) (and the corresponding dI/dV) response. This is the more relevant comparison with experimental results. For example, the electric field in the tip−sample gap depends on the bias voltage and the tip−sample distance, which, in turn, change during the spectroscopy experiment as the bias voltage is varied, and the feedback changes the tip−sample distance to maintain a constant tunneling current. In the theoretical model, the potential barrier between the tip and the sample determines the tunneling current. We solve this from a 1D transmission problem. On one side of the potential, the wave function is a plane-wave propagating away from the barrier. Starting from this, one can numerically integrate the B


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It can be seen that the peak position is essentially invariant with position. There is a slight overall shift on the order of 20 mV; consecutive measurement points are within 5 mV from each other. This indicates that we can readily measure sub-10 meV shifts of the local work function. The response on SiO2 is markedly different (Figure 3b). The energy of the first FER varies significantly with the position on the sample, and changes of >100 mV within the scan were detected, as shown in Figure 3b. Both of the peaks of this split resonance shift similarly, which can be expected as FER position depends on the overall work function. These shifts are related to the well-known presence of charge puddles on G/ SiO2, which are significantly suppressed on G/h-BN. The magnitude of the shifts we measure on h-BN and SiO2 are consistent with the magnitude of the charge puddles and their expected length scales reported in the literature.18,23−25 More careful inspection reveals further details in the spectra shown in Figure 3b. On certain spots on the G/SiO2 surface, the FERs disappear; that is, their amplitude is below the detection limit of our measurement. This was not observed on G/h-BN, where the measurements are extremely reproducible. This is investigated in more detail in Figure 4, which shows an

Schrödinger equation to the other side of the potential, where one can match the solution with the incident and reflected plane waves. From these, the transmission coefficient can be calculated. The transmission integrated over the bias voltage is proportional to the tunneling current. In line with the experiment, the simulation starts with a given bias voltage and tip height and directly simulates a constant current experiment: As the bias is increased, there is a matching increase in the tip height to keep the current constant. The model naturally includes both the contributions of direct tunneling (nonresonant tunneling) and resonant tunneling through the image-potential states. Roughly speaking, the overall slope of the z(V) curve is given by the nonresonant tunneling, while the steps naturally correspond to tunneling through the FERs. As the simplest possible model potential, we consider graphene as a square-well potential (Figure 2a). The depth and the width of the square-well have a relatively minor effect on the FER resonances; they mostly affect the shape of the first FER slightly. This is due to the fact that for reasonable well parameters (width ca. 4 Å) the FER wave functions have the highest intensity outside the graphene and are only slightly modified by the potential well shape. Deriving more realistic model potentials from, for example, first-principle calculations, would be possible; however, already the simple model potential is able to reproduce the experimentally measured z(V) curve extremely well (Figure 2b). One should note that a more realistic model potential would also need to be rather complicated and nonlocal as it would need to take into account the orthogonality to the occupied states of the graphene. Additionally, the overall slope of the z(V) curve and the spacing of the higher order FERs depends mostly on parameters related to the tip shape. The tip can be simply modeled as a metallic sphere with a radius R0. Reducing the tip radius results in a steeper slope of z(V) curves at high bias, and the spacing between the higher order FERs is decreased. This is due to the increased nonlinearity of the potential profile in the tip−substrate gap. According to the results from the present model, in agreement with previous literature,6,7,9 the position of the FERs is controlled by the sample work function, indicating that the FERs can be used to map out variations of the local work function. We use this to study the local variations of the work function of G/h-BN and G/SiO2 (Figure 3). Figure 3a shows spectra along a line spanning several G/h-BN moiré unit cells.

Figure 4. (a) Topographic image of the G/SiO2 sample. (b) Constant current spectra measured from bottom to top in the direction of the blue arrow in panel a. The scale bar is 3 nm.

example of an area on G/SiO2 with regions where FERs are not observed. The constant-current dI/dV spectra have been measured along the blue arrow in Figure 4a. In general, the amplitude of the FERs is related to the relative magnitudes of direct tunneling between the tip and graphene and tunneling through the field-emission resonances. Reducing the overlap between the FER and tips states (by analogy to the difference between the n- and m-series) results in a reduction of the peak amplitudes in the dI/dV spectra until they are below what we can experimentally resolve. These local changes are likely to be related to the increased disorder in G/SiO2 compared with G/ h-BN due to, for example, impurities trapped between graphene and the SiO2 substrate or local bonding between graphene and SiO2 and the resulting rehybridization of the graphene states. This conclusion is further supported by several accounts on the superiority of h-BN as a substrate for graphene compared with SiO2.18,20

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Figure 3. Measured dI/dV in gray scale over the bias range covering the first FER taken along the line indicated in the corresponding topography image (bottom). The measurements are carried out on G/ h-BN (a) and G/SiO2 (b). Scale bars are 2 nm.

CONCLUSIONS In summary, FER measurements were done on G/h-BN and G/SiO2 surfaces. FERs on G/h-BN can be quantitatively C


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scale in transition metal-supported graphene. ACS Nano 2010, 4, 5773−5782. (12) Borca, B.; Barja, S.; Garnica, M.; Sánchez-Portal, D.; Silkin, V. M.; Chulkov, E. V.; Hermanns, C. F.; Hinarejos, J. J.; Vázquez de Parga, A. L.; Arnau, A.; et al. Potential energy landscape for hot electrons in periodically nanostructured graphene. Phys. Rev. Lett. 2010, 105, 036804. (13) Craes, F.; Runte, S.; Klinkhammer, J.; Kralj, M.; Michely, T.; Busse, C. Mapping image potential states on graphene quantum dots. Phys. Rev. Lett. 2013, 111, 056804. (14) Li, X. S.; Cai, W. W.; An, J. H.; Kim, S.; Nah, J.; Yang, D. X.; Piner, R.; Velamakanni, A.; Jung, I.; Tutuc, E.; et al. Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 2009, 324, 1312−1314. (15) Kang, J.; Shin, D.; Bae, S.; Hong, B. H. Graphene transfer: Key for applications. Nanoscale 2012, 4, 5527−5537. (16) Stolyarova, E.; Rim, K. T.; Ryu, S. M.; Maultzsch, J.; Kim, P.; Brus, L. E.; Heinz, T. F.; Hybertsen, M. S.; Flynn, G. W. Highresolution scanning tunneling microscopy imaging of mesoscopic graphene sheets on an insulating surface. Proc. Natl. Acad. Sci. U. S. A. 2007, 104, 9209−9212. (17) Ishigami, M.; Chen, J. H.; Cullen, W. G.; Fuhrer, M. S.; Williams, E. D. Atomic structure of graphene on SiO2. Nano Lett. 2007, 7, 1643−1648. (18) Xue, J.; Sanchez-Yamagishi, J.; Bulmash, D.; Jacquod, P.; Deshpande, A.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P.; LeRoy, B. J. Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nat. Mater. 2011, 10, 282−285. (19) Yankowitz, M.; Larentis, S.; Kim, K.; Xue, J.; McKenzie, D.; Huang, S.; Paggen, M.; Ali, M. N.; Cava, R. J.; Tutuc, E.; et al. Intrinsic disorder in graphene on transition metal dichalcogenide heterostructures. Nano Lett. 2015, 15, 1925−9. (20) Järvinen, P.; Hämäläinen, S. K.; Banerjee, K.; Häkkinen, P.; Ijäs, M.; Harju, A.; Liljeroth, P. Molecular self-assembly on graphene on SiO2 and h-BN substrates. Nano Lett. 2013, 13, 3199−3204. (21) Gwyddion. http://gwyddion.net/. (22) Yankowitz, M.; Xue, J.; Cormode, D.; Sanchez-Yamagishi, J. D.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P.; Jacquod, P.; LeRoy, B. J. Emergence of superlattice dirac points in graphene on hexagonal boron nitride. Nat. Phys. 2012, 8, 382−386. (23) Deshpande, A.; Bao, W.; Miao, F.; Lau, C. N.; LeRoy, B. J. Spatially resolved spectroscopy of monolayer graphene on SiO2. Phys. Rev. B: Condens. Matter Mater. Phys. 2009, 79, 205411. (24) Decker, R.; Wang, Y.; Brar, V. W.; Regan, W.; Tsai, H.-Z.; Wu, Q.; Gannett, W.; Zettl, A.; Crommie, M. F. Local electronic properties of graphene on a bn substrate via scanning tunneling microscopy. Nano Lett. 2011, 11, 2291−2295. (25) Zhang, Y.; Brar, V. W.; Girit, C.; Zettl, A.; Crommie, M. F. Origin of spatial charge inhomogeneity in graphene. Nat. Phys. 2009, 5, 722−726. (26) Kretinin, A. V.; Cao, Y.; Tu, J. S.; Yu, G. L.; Jalil, R.; Novoselov, K. S.; Haigh, S. J.; Gholinia, A.; Mishchenko, A.; Lozada, M.; et al. Electronic properties of graphene encapsulated with two different twodimensional atomic crystals. Nano Lett. 2014, 14, 3270−3276. (27) Geringer, V.; Liebmann, M.; Echtermeyer, T.; Runte, S.; Schmidt, M.; Ruckamp, R.; Lemme, M. C.; Morgenstern, M. Intrinsic and extrinsic corrugation of monolayer graphene deposited on SiO2. Phys. Rev. Lett. 2009, 102, 076102. (28) Mashoff, T.; Pratzer, M.; Geringer, V.; Echtermeyer, T. J.; Lemme, M. C.; Liebmann, M.; Morgenstern, M. Bistability and oscillatory motion of natural nanomembranes appearing within monolayer graphene on silicon dioxide. Nano Lett. 2010, 10, 461−465.

interpreted with a simple 1D model. Surprisingly, on the G/ SiO2 sample, the first resonance was split into two distinct components, and at some points on the sample, it was not observed at all. We attribute these effects to the increased disorder in graphene compared with the G/h-BN surface. This was also reflected on the measured energy variations of the FERs on the two samples, which are caused by local changes of the sample work function. G/SiO2 shows at least an order of magnitude larger variation in the local work function due to the presence of charge puddles. On both samples, the position of the FERs can be used to map out the local work function of the sample with high energy and spatial resolution.

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AUTHOR INFORMATION

Corresponding Author

* E-mail: peter.liljeroth@aalto.fi. Notes


The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research made use of the Aalto Nanomicroscopy Center (Aalto NMC) facilities and was supported by the European Research Council (ERC-2011-StG No. 278698 “PRECISENANO”) and the Academy of Finland (Centres of Excellence in Low Temperature Quantum Phenomena and Devices No. 250280 and in Computational Nanoscience No. 251748). We acknowledge the computational resources provided by Aalto Science-IT project and Finland’s IT Center for Science (CSC).

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REFERENCES

(1) Niesner, D.; Fauster, T. Image-potential states and work function of graphene. J. Phys.: Condens. Matter 2014, 26, 393001. (2) Crampin, S. Lifetimes of stark-shifted image states. Phys. Rev. Lett. 2005, 95, 046801. (3) Fowler, R. H.; Nordheim, L. Electron Emission in Intense Electric Fields. Proc. R. Soc. London, Ser. A 1928, 119, 173−181. (4) Binnig, G.; Frank, K. H.; Fuchs, H.; Garcia, N.; Reihl, B.; Rohrer, H.; Salvan, F.; Williams, A. R. Tunneling spectroscopy and inverse photoemission: Image and field states. Phys. Rev. Lett. 1985, 55, 991− 994. (5) Kolesnychenko, O. Y.; Kolesnichenko, Y. A.; Shklyarevskii, O.; van Kempen, H. Field-emission resonance measurements with mechanically controlled break junctions. Phys. B 2000, 291, 246−255. (6) Pivetta, M.; Patthey, F.; Stengel, M.; Baldereschi, A.; Schneider, W.-D. Local work function moiré pattern on ultrathin ionic films: NaCl on Ag(100). Phys. Rev. B: Condens. Matter Mater. Phys. 2005, 72, 115404. (7) Ploigt, H.-C.; Brun, C.; Pivetta, M.; Patthey, F.; Schneider, W.-D. Local work function changes determined by field emission resonances: NaCl/Ag(100). Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 76, 195404. (8) Ruffieux, P.; Aït-Mansour, K.; Bendounan, A.; Fasel, R.; Patthey, L.; Gröning, P.; Gröning, O. Mapping the electronic surface potential of nanostructured surfaces. Phys. Rev. Lett. 2009, 102, 086807. (9) Schulz, F.; Drost, R.; Hämäläinen, S. K.; Demonchaux, T.; Seitsonen, A. P.; Liljeroth, P. Epitaxial hexagonal boron nitride on Ir(111): A work function template. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89, 235429. (10) Yang, H.; Baffou, G.; Mayne, A. J.; Comtet, G.; Dujardin, G.; Kuk, Y. Topology and electron scattering properties of the electron interfaces in epitaxial graphene probed by resonant tunneling spectroscopy. Phys. Rev. B: Condens. Matter Mater. Phys. 2008, 78, 041408. (11) Wang, B.; Caffio, M.; Bromley, C.; Früchtl, H.; Schaub, R. Coupling epitaxy, chemical bonding, and work function at the local D


Field-Emission Resonances on Graphene on Insulators - The Journal

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