Coherent thermoelectric power from graphene quantum dots - Nano

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Coherent thermoelectric power from graphene quantum dots Mali Zhao, Dohyun Kim, Van Luan Nguyen, Jinbao Jiang, Linfeng Sun, Young Hee Lee, and Heejun Yang Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b03208 • Publication Date (Web): 21 Dec 2018 Downloaded from http://pubs.acs.org on December 21, 2018

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Coherent thermoelectric power from graphene quantum dots Mali Zhao,† Dohyun Kim,† Van Luan Nguyen,‡ Jinbao Jiang,†,‡ Linfeng Sun,† Young Hee Lee,†,‡ and Heejun Yang†* †Department ‡IBS

of Energy Science, Sungkyunkwan University, Suwon 16419, Korea

Center for Integrated Nanostructure Physics (CINAP), Institute for Basic Science,

Sungkyunkwan University, Suwon 16419, Korea

ABSTRACT: The quantum confinement of charge carriers has been a promising approach to enhance the efficiency of thermoelectric devices, by lowering the dimension of materials and raising the boundary phonon scattering rate. The role of quantum confinement in thermoelectric efficiency have been investigated using macroscopic device-scale measurements based on diffusive electron transport with the thermal de Broglie wavelength of the electrons. Here, we report a new class of thermoelectric operation originating from quasi-bound state electrons in low dimensional materials. Coherent thermoelectric power from confined charges were observed at room temperature in graphene quantum dots with diameters of several nanometers. The graphene quantum dots, electrostatically defined as circular n-p-n junctions to isolate charges in the p-type graphene quantum dots, enabled thermoelectric microscopy at atomic scale, revealing weakly

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localized and coherent thermoelectric power generation. The conceptual thermoelectric operation provides new insights, selectively enhancing coherent thermoelectric power via resonant states of charge carriers in low dimensional materials.

KEYWORDS: quantum confinement, graphene quantum dots, coherent thermoelectric power, quasi-bound state electrons, thermoelectric applications

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Thermoelectric power generation holds great promise as a renewable energy technology. Thermoelectric efficiency is described by the dimensionless figure of merit, ZT=S2ıț-1T, where S is the Seebeck coefficient, ı is the electrical conductivity, ț is the thermal conductivity, and T is the absolute temperature. State-of-the-art commercial thermoelectric materials such as Bi2Ti3 have reached a room temperature ZT of around 1, and extensive efforts to further improve thermoelectric efficiency have been proposed using low dimensional materials and nanostructuring.1-5 In particular, studies have introduced dense interfaces with a length scale comparable to the phonon mean-free path to effectively reduce the heat flow carried by the crystal lattice.6, 7 Despite these efforts, we note that previous studies have only considered diffusive electron transport and the thermal de Broglie wavelength of the electrons in reduced (low) dimension to improve the ZT or Power factor, PF=S2ı. The role of bound state electrons, which inevitably appear in nanometer-scale materials, in achieving novel thermoelectric performance has not been investigated, largely because appropriate methodologies, such as thermoelectric microscopy and atomically clean nanometer-scale thermoelectric materials, have been lacking. The graphene quantum dot (QD) is an ideal model system for building a conceptual framework for novel thermoelectric systems with reduced dimensions (both the thickness and the lateral size) and increased boundary scattering of phonons.8 Besides the pristine electronic band structure of graphene, which can determine its typical thermoelectric performance, quasi-bound states of Dirac fermions have been reported in graphene QDs.9, 10 The graphene QDs can trap electrons and generate spatial resonance modes. The thermoelectric features resulting from the trapped electrons, based on their coherent scattering and weak localization, clearly contrasts with the conventional use of QDs embedded in bulk material11, 12 or nanowires13 for higher thermoelectric power (TEP).

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Thermoelectric imaging by scanning thermoelectric microscopy (SThEM) has revealed atomic-scale structural disorders in epitaxial graphene on silicon carbide.14 The technique is based on the fact that local thermoelectric PF or S sensitively reflects the local electronic structure of the epitaxial graphene14 near the Fermi energy (with an energy window of ~100 meV). The Seebeck coefficient is proportional to the logarithmic energy derivative of the local density of states (LDOS) at the Fermi level, which can be sensitively probed by SThEM at room temperature, as compared with scanning tunneling microscopy/spectroscopy (STM/STS). We further note that the tunneling transport in STM/STS inevitably involves phonon-assisted inelastic scattering15 which prevents the precise study of the electronic structure of graphene near the Fermi energy, which is a critical issue for the thermoelectric study of graphene. The SThEM technique intuitively measures the local TEP of materials, and the charge carrier type and the local Seebeck coefficient (S) can be probed with an atomic resolution.14, 16, 17 In this study, circular graphene QDs with diameters of less than 5 nm were synthesized by a post annealing of chemical vapor deposition (CVD) grown graphene on Cu foil with a temperature near the melting temperature of Cu. The graphene QDs, continuously connected to the outside graphene without edge disorders, allow the resonant TEP modes to be investigated. The variable temperature scanning probe microscopy (VT-SPM, Omicron XA), which can separately anneal the sample while keeping the tip at room temperature, was used for TEP imaging. We discovered enhanced coherent TEP originating from the resonant states of confined charge carriers or the short-range LDOS variation in graphene QDs near the Fermi level. Creating such sub-bands or resonant modes with coherent wavefunctions of highly mobile carriers in graphene QDs has a potential for efficient quantum (ballistic) transport and ultimate thermoelectric performances of

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nanoscale materials. This provides a strategy to enhance the thermoelectric performance via selective coherent resonant states in two-dimensional materials.

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Sample preparation and STM characterization. Graphene was grown by CVD on copper (Cu) foil and then the sample was post-annealed with a temperature near the melting temperature of Cu to synthesize atomically clean graphene QDs, similar to a previous report.10 The post annealing (T=1100 K for 30 minutes) produces surface reconstruction of the Cu, covered by singlelayer graphene (SLG),18, 19 as shown in Figure 1a. The topography and the electronic structure of the graphene were modified by the post-annealing, as probed by STM/STS (Figure 1b-f). While the SLG shows a flat topography (Figure 1b) on Cu terraces before the post-annealing, after the post-annealing the SLG shows striped patterns with a period of 16.8 nm and average height of 0.21 nm (Figure 1c), which is smaller than the Cu atomic steps (0.36 nm). The generation of the striped patterns during the post-annealing can be understood to result from compressive strain applied to the Cu surface, due to the different thermal expansion coefficients of graphene and Cu.20-22 An atomic scale image after the post-annealing in Figure 1d exhibits the hexagonal atomic structure of the SLG with a linear Moiré pattern of 1.03 nm, which can be simulated as a 2.5° rotation between graphene zigzag and the [1,-1,0] direction of Cu (331). The high index facet of Cu was confirmed by X-ray diffraction and Electron Backscatter Diffraction (Figure S1b, c). Tunneling spectroscopy of the SLG exhibits a shift in the graphene’s Dirac point from -0.15 V to -0.27 V (Figure 1f), indicating higher electron doping following the post-annealing, probably due to stronger interaction with the Cu substrate, and a higher compressive strain in the graphene.23-25

SThEM set-up and thermoelectric imaging of graphene terraces. The SThEM using atomic force microscopy (AFM) in contact mode revealed a local TEP variation in the SLG covering various Cu step edges, which has been limited by other tools such as STM/STS at room temperature. For SThEM, a platinum-coated cantilever and a temperature difference of ǻT=30 K

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between the SLG and the tip were used, as shown in Figure 2a. The thermoelectric voltage (ǻV) through the vicinity of the contact changes with the temperature difference (ǻT). The absolute value of thermoelectric voltage does not all depend on the generated thermoelectric voltage at the tip-sample interface, but it is also affected by the diffusive thermoelectric voltages both at the tip and sample as well as the possible thermoelectric voltage in experimental set-up (e.g. junctions between cables and electrodes or other piezo parts). Therefore, the voltage measured in SThEM is not the absolute value of thermoelectric voltage generated at the tip-sample interface. However, the variation of the thermoelectric voltage is meaningful, which can precisely reflect the position dependent thermoelectric power variation of the sample surface. Figure 2b shows the thermoelectric voltage of the SLG on Cu as a function of the temperature difference between the tip and the SLG. A Seebeck coefficient of -20.3 ȝV/K could be determined from the ǻV-ǻT slope in Figure 2b, similar to the macroscopically measured Seebeck coefficient of SLG on Cu foil at room temperature.26 In addition, the negative value of S indicates overall ntype doping of the SLG interacting with the Cu substrate, consistent with the STS (Figure 1f) and Raman spectroscopy results (Figure S2). The topography and the corresponding thermoelectric voltage ǻV or TEP mapping were obtained simultaneously across the Cu surface steps as shown in Figure 2c, d. The subtle variation in the local electronic structure or TEP of the SLG can be investigated with high energy (~100 meV) and high spatial (0.1 nm) resolution, since the TEP of a material can be expressed by the formula below: ಢ౜

ଵ ‫୒ ׬‬ሺ୉ሻቀିಢుቁሺ୉ି୉ూ ሻୢ୉

ൌ െ ȁୣȁ୘

ಢ౜

‫୒ ׬‬ሺ୉ሻቀିಢుቁୢ୉

‫ ן‬െܶ

ௗ௟௡ேሺாሻ ௗா

(1)

where T is the absolute temperature, N(E) is the density of states (DOS) of the charge carriers, (െ

ப୤

) is the negative derivative of the Fermi-Dirac distribution function at temperature T.16 At

ப୉

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ப୤

low temperature, the (െ ப୉) is approximated to be a Dirac delta function, which is symmetric with respect to the Fermi level with a width about 3.5 times kBT (kBT§25 meV at T=300 K). The sign of the TEP depends on the majority charge carrier type, which is negative (positive) for electrons (holes). The magnitude of TEP is correlated to the energy derivative of the DOS near the Fermi level. The negatively enhanced ǻV near the Cu step edges in the inset of Figure 2d indicates a variation in the electronic structure of the graphene across the Cu steps. The TEP of graphene increases as the Fermi level moves toward the Dirac point.27, 28 Compared with the n-type doping of graphene on a flat Cu terrace, weaker coupling between the graphene and Cu due to graphene detachment on the Cu steps shifts the Fermi level closer to the Dirac point (as shown in Figure S5) and results in a negative enhancement of TEP28. Similar TEP variation has been observed across the boundary between monolayer and bilayer graphene on SiC substrate.17 However, the clear local TEP variation in the SLG covering metallic substrate steps (highlighted in the inset of Figure 2d) reveals the potential of SThEM as an ideal tool for directly studying thermoelectric features using nanostructures.

Observation of resonant TEP modes in graphene QDs by SThEM. On flat terraces of SLG where AFM topography showed no structural disorders (Figure 3a), wave-like resonant patterns with radii from 1.8 nm to 2.3 nm were observed with (simultaneously obtained) TEP mapping, as shown in Figure 3b. The subtle graphene ripples in Figure 3b are consistent with the morphology shown in Figure 3a, which confirms the reliability of our SThEM. Because the atomic-scale concentric resonant patterns with an abrupt edge and a small radius only appear in the TEP mapping (Figure 3b and 3c), carbon atomic defects in graphene could be excluded as the origin of

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the resonant patterns. Moreover, no inter-valley scattering in graphene can be observed in the Fast Fourier Transform (FFT) pattern (Figure 3d), which supports the absence of sharp atomic defects on the terrace of the SLG.29, 30 The concentric circular standing waves were also reported due to Friedel oscillations of Cu (111) surface state near defects.31, 32 Whereas, the facet of Cu in our experiment is anisotropic (331) instead of isotropic (111), as confirmed by XRD and EBSD in Figure S1b and S1c. Therefore, the possibility of standing waves owing to Cu surface state is also ruled out.33, 34 The resonant patterns obtained by SThEM, in Figure 3b, c, can be understood to be resonant TEP modes from the quasi-bound states of Dirac fermions inside circularly-defined graphene QDs. Given the overall n-type doping characteristics of our graphene on Cu, the quasi-bound states or the resonant states only arise with local p-type doping of graphene.9, 10 The schematic model for the circularly-defined graphene QD and the potential barrier for trapped holes in the p-type graphene QD are shown in Figure 3e; electrons in the valence band of the graphene inside the graphene QD encounter a potential barrier to conserve the sublattice isospin (red or blue lines in Figure 3e), illustrated by the black-dotted line in Figure 3e. Despite the Klein tunneling of Dirac fermions through potential barriers in graphene, it has been discovered that quasi-bound states of electrons appear in circularly-defined p-type graphene QDs on Cu, when prepared by a postannealing similar to our method.10 Surface reconstruction of the Cu (331) by the post-annealing could induce the local potential variation in the graphene QDs. The physical nature of the resonant TEP modes of the quasi-bound states probed by SThEM can be described by the radial and angular momentum quantum numbers of the electrons at the Fermi level (with an energy window of 100 meV) as well as the size of the graphene QDs. In order to observe the resonant quasi-bound states by SThEM, the resonant energy and the Fermi level

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with respect to the Dirac point should be matching. The resonant states have finite energy widths given by Ɂ ൌ ԰Ȁɒ where Ɂ is the full-width at half maximum of the resonant mode, ԰ is Planck’s constant h divided by 2ʌ, and Ĳ is the trapping time of the confined electrons.10 According to the previous study, the trapping time and the resonant energy width with a radius of 2.1 nm are estimated to be 4 femtoseconds (fs) and 150 meV. The large resonant energy width (150 meV) and the probing energy window of the SThEM (100 meV) facilitates the observation of the resonant patterns in Figure 3b and 3c (also see details in Figure S3a). We present the amplitude profile of the resonant TEP modes across a graphene QD (following the red line in Figure 3c) with a schematic interpretation in Figure 3f. The complex interior nodal pattern in Figure 3f can be understood as two degenerate quasi-bound states at the Fermi level in our graphene QD.9 Since lower energy states are more likely to be observed with longer trapping time, we interpret that the resonant TEP modes in Figure 3f originate from the two lowest degenerate eigenstates, ȥn,1/2 and ȥn-1,5/2, where ȥn,m represents the eigenstate with radial (n) and angular momentum (m) quantum numbers in the graphene QD,9 as shown in Figure S3b. The p-type characteristic and the potential barrier height for the graphene QD were supported by STM/STS, as shown in Figure 4. Several randomly distributed graphene QDs with an average radius of 4.98nm are observed by STM. Although the resonant patterns are not as clear as in the TEP mapping (Figure 3b), the result of tunneling spectroscopy inside the QDs can be compared to that of the surrounding graphene to estimate the barrier height. A gap-like feature (EF±70 meV) from inelastic scattering in graphene is present,15 as highlighted by the orange rectangle in Figure 4b. Defining the local minimum in the tunneling spectroscopy as the location of the Dirac point (Figure 4b), the Fermi level of the n-type SLG on Cu is at 0.24 eV above the Dirac point (blue), while the Fermi level of the graphene QD is found to be at 0.21 eV below the Dirac point (red);

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this indicates the potential barrier height of the QD with the surrounding n-type graphene is 0.45 eV, which is similar to the previous value in graphene QDs.10 In addition, a resonant peak at 31 meV below the Fermi level (within inelastic scattering energy range) is detected inside the graphene QDs, which can be attributed to the lowest resonant state due to the confined charge carriers in graphene QDs. The bound state near the Fermi level enables the coherent thermoelectric power mapping in SThEM. For the circular graphene QDs with different radii, the energy of the resonant states is inversely related to the radius of the QDs. The detected energy of the lowest resonant state (31 meV away from the Fermi level) in the graphene QDs with a radius of 4.98 nm (Fig. 4) is lower than the first resonant state (70 meV) in graphene QDs with a radius of 2.1 nm (Fig. 3); this confirms that the origin of the coherent thermoelectric power in SThEM is the bound states of graphene QDs near the Fermi level. We further note that the bound states near the Fermi level compete with the gap-like feature induced by inelastic tunneling, making them hard to be detected by STS; it is easier to probe the resonant states by SThEM. Besides the resonant patterns, small dark spots with a radius of 0.8 nm are also observed on the flat terraces of the SLG in the TEP mapping (Figure 5a, b). Larger area topography and TEP mapping images are shown in Figure S4. The magnification of one dark spot with a linear Moiré pattern in TEP mapping with atomic resolution is shown in Figure 5c. The carbon lattice is continuous across the dark region, but there is no resonant feature like the one shown in Figure 3. The TEP profile along the red dotted line in Figure 5c shows a higher TEP (from electrons) at the center of the dark spot in Figure 5d. We interpret the smaller dark spots in the TEP mapping in two ways. First, the dark spot regions have different doping states, due to substrate defects, compared to the surrounding region, but they still retain an n-type doping characteristic. In this case, the electrons cannot be freely

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reflected at the boundary, and quasi-bound states cannot be formed inside the boundary (Figure 5e, f). Accordingly, the SThEM probes of the less n-type doped graphene region showed a higher negative TEP. The other possibility is that the defects in the top Cu surface or between the SLG and top Cu surface may create a defect state in graphene slightly above the Fermi level, which induces an abrupt positively increased LDOS’ near the Fermi level and therefore, a negative enhancement of TEP.14 To summarize, we introduce novel coherent TEP generated from confined and resonant charges in two dimensional graphene QDs. Specifically, graphene QDs with quasi-bound state electrons with radii of 2 nm to 5 nm were synthesized using a post-annealing process, and their TEP at room temperature were imaged at atomic-scale using SThEM. The coherent TEP is generated by resonant states of confined charge carriers in two dimensional graphene QDs. For practical applications, creating QDs or bound states in two dimensional graphene can make the effective mass of electrons increased, which makes the thermal de Broglie wavelength of electrons decreased and the power factor enhanced.4 Moreover, like defects or grain boundaries, the lattice thermal conductivity near graphene QDs could be reduced. Therefore, an improvement of thermoelectric performance is expected by creating QDs in graphene sheet. Creating QDs in low dimensional materials and the TEP quantification at atomic-scale by SThEM offer a new insight into the enhancement of thermoelectric performance for future energy applications.

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Experimental Section Sample synthesis. The single layer graphene (SLG) domains were grown on polycrystalline Cu foil by Chemical Vapor Deposition (CVD). First, a100-μm-thick copper foil was polished with the chemical-mechanical polishing (CMP) method to remove the amorphous copper oxide. The sample was placed in a quartz tube chamber and heated up to T=1300 K under Ar (1000 sccm) and H2 (200 sccm) environment for 2 hours to completely remove the residual defects on the copper surface. After that, the H2 gas was reduced to 35 sccm and CH4 gas was injected at 25 sccm for 30 min to produce hundreds of hexagonal flakes of SLG with different orientations on Cu foil. Subsequently, the CH4 was turned off and the chamber was cooled to room temperature naturally. After this growth, the sample was transferred into a variable temperature scanning probe microscope (VT-SPM) and annealed at T=673 K in vacuum to remove the adsorbed water and other contaminations. To synthesize the graphene QDs, the sample was further annealed at T=1100 K for 30 min. Raman spectroscopy. Raman spectroscopy of both pristine and high-temperature annealed graphene samples was conducted using a Renishaw Raman Microscope at room temperature in ambient conditions. A laser wavelength of 532 nm and a grating of 1800 were used. Before measurement, the Raman spectroscopy was calibrated using the SiO2 standard peak at a frequency of 520 cm-1. More than five single point spectrum curves were taken and averaged to obtain valid Raman data. X-ray diffractometer (XRD). A Smartlab XRD featuring the PhotonMax high-flux 9 kW rotating anode X-ray source coupled with a HyPix-3000 high-energy-resolution was used in this experiment. To determine the crystal surface index of the polycrystalline Cu after the high

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temperature annealing for STM and SThEM scanning, the powder mode XRD with a long range tracking angle (2ș) from 20° to 160° was employed for the measurement. Electron backscatter diffraction (EBSD). The JSM7000F mode EBSD with a resolution of 3.0nm was used to locally verify the dominant orientation of the Cu substrate after high temperature annealing in the scanning region. Scanning tunneling microscopy (STM). Before TEP imaging, the SLG on Cu were characterized by STM before and after the post-annealing. All STM measurements were carried out at room temperature with a chemically etched tungsten tip. The scanning tunneling spectroscopy (STS) was conducted with a lock-in preamplifier. Scanning thermoelectric microscopy (SThEM). The SThEM was achieved using a modification of ultra-high vacuum contact mode AFM. In this experiment, the sample was heated and the cantilever was kept at room temperature. At the tip-sample interface, the radiative heat transfer near the tip edge can be negligible35. The only possible heat transfer is the conduction between tip probe and sample at the localized contact area, which strongly depends on the thermal coupling between tip and sample, in other words, the interaction force between tip and sample. Due to the linear correlation of temperature drop at tip-sample interface and the interaction force (Lenard-Jones potential) between tip and sample16, the soft contact between tip and sample in our experimental set-up (reference force is in the range of 10-9 to 10-12 N) guarantees the small temperature drop at the tip-sample interface, that is less than 2% of the total delta T.14, 36 As a result, the temperature difference at the tip-sample interface could be precisely controlled. A high impedance voltmeter (Keithley 6517B electrometer with an input impedance higher than 200 Tȍ) was connected between the grounded sample and the Pt-coated cantilever to measure the TEP. During the experiment, the repulsive force feedback loop is on, the temperature difference between 14


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the tip and sample is kept constant, therefore, the topography and thermoelectric voltage can be obtained simultaneously using the contact mode AFM and SThEM.

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ASSOCIATED CONTENT Supplementary information including characterization of crystal orientations of polycrystalline Cu foil after annealing at 1100 K, Raman spectroscopy for graphene on Cu foil before and after annealing in vacuum at 1100 K, Eigenstates of Dirac Fermions in circular graphene quantum dots (QDs) and the correlation with the resonant TEP modes in SthEM, the thermoelectric imaging of large scale SLG on Cu foil after annealing at 1100 K as well as the STS of SLG across the nanometer-scale Cu step. (PDF)

AUTHOR INFORMATION Corresponding author * Email: [email protected] ORCID Mali Zhao: 0000-0001-6282-3596 Dohyun Kim: 0000-0002-0758-6281 Heejun Yang: 0000-0003-0502-0054

Notes The authors declare no completing financial interests.

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ACKNOWLEDGMENTS This work is supported by National Research Foundation of Korea (NRF) under Grant No. NRF2017R1A2B2008366. Authors Young Hee Lee, Van Luan Nguyen, and Jinbao Jiang acknowledge the support from the Institute of Basic Science (IBS-R011-D1). Authors Linfeng Sun received funding from the NRF supported by the Ministry of Science and ICT under grant no. NRF2017H1D3A1A01013759. Authors Heejun Yang, Mali Zhao and Dohyun Kim received funding from NRF under Grant No. NRF-2017R1A2B2008366.

ABBREVIATIONS QD, quantum dot; TEP, thermoelectric power; SThEM, scanning thermoelectric microscopy; LDOS, local density of states; STM, scanning tunneling microscopy; STS, scanning tunneling spectroscopy; S, seebeck coefficient; CVD, chemical vapor deposition; Cu, copper; SLG, single layer graphene; DOS, density of state; AFM, atomic force microscopy; CMP, chemicalmechanical polishing; VT-SPM, scanning probe microscope; XRD, X-ray diffractometer; EBSD, Electron backscatter diffraction

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Figures

Figure 1. The sample preparation schematic and STM characterization. (a) Experimental procedures of synthesizing SLG and graphene QDs on Cu foil. (b) Typical STM topography of pristine CVD grown SLG. Tunneling condition: Vs=-1.0 V, I=1.0 nA. (c) Typical STM topography of the SLG after the post-annealing at T=1100 K. Tunneling condition: Vs=-0.5 V, I=0.5 nA. (d) A 5 nm × 5 nm atomic scale STM image of graphene after annealing at 1100 K, tunneling condition: Vs=-0.3 V, I=0.6 nA. The hexagonal structure confirms a single layer of graphene, and the moiré pattern shows a quasi-one dimensional feature with a period of 1.03nm. (e) A schematic model of the moiré pattern in Panel e simulated by rotating 2.5° between the graphene zigzag direction and the [1,-1,0] direction of Cu (331). (f) The dI/dV curves of SLG before (black) and after the post-annealing (red). The Dirac point is shifted from -0.15 eV to -0.27 eV with respect to Fermi level.

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Nano Letters

Figure 2. Schematic of the thermoelectric imaging set-up and the typical thermoelectric mapping on SLG terraces. (a) The schematic of SThEM modified by a UHV contact-mode AFM. In this set-up, the sample is grounded and slightly heated, while the conductive cantilever is kept at room temperature, the thermoelectric voltage is measured by a high-impedance voltmeter in an independent open circuit. The topography and thermoelectric voltage images can be obtained simultaneously by normal AFM scanning. (b) The spectroscopic measurement of thermoelectric voltage of SLG on polycrystalline Cu as a function of applied temperature difference between tip and sample. The linear slope of ǻV-ǻT curve shows a negative Seebeck coefficient of graphene on Cu (S=-20.3 μV/K), confirming the n-doping of graphene in STS. (c) Typical contact-mode AFM topography of the SLG. The sample temperature was kept at T=330 K (ǻT=30 K). Scanning condition: a contact force of 1.5 nN and a pixel raster time of 930 ȝs. (d) The simultaneously obtained TEP mapping with ‘c’. The TEP was negatively enhanced near the Cu steps

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Figure 3. Resonant thermoelectric power in circular graphene quantum dots. (a) AFM topography of a flat terrace of SLG without structural defects. (b) The simultaneously obtained TEP mapping. Scanning condition: ǻT=30 K, a contact force of 0.005 nN, and a pixel raster time of 20 ms. Several circular resonant features appear with a radius from 1.8 nm to 2.3 nm. (c) A 10 nm × 10nm zoom of a resonant TEP pattern. (d) The Fast Fourier Transform (FFT) pattern of the resonant TEP pattern in panel ‘c’. The line-shaped spots represent the graphene hexagonal lattice, the concentric circles around Ƚ denote the standing wave pattern (Both the line-shaped spots and ellipse around Ƚ are due to the thermal drift). (e) A schematic model of the Cu surface reconstruction to induce local n-p-n graphene QDs and the energy band diagram across the graphene QD. (f) The TEP amplitude profile following the red-dotted line in ‘c’, which exhibits the maxima both in the center and concentric ring of graphene QD. In the right panel, two degenerate wavefunctions (ȥn,1/2, ȥn1,5/2)

are described for matching the TEP profile in the left side.

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Nano Letters

Figure 4. Characterization of graphene QDs by STM and STS. (a) STM topography showing multiple nanometer scale circular graphene QDs. No obvious resonant features are observed. Tunneling condition: Vs=-0.5 V, I=1.0 nA. (b) A comparison of the dI/dV spectra of graphene QDs (red curve) and the surrounding graphene (blue curve). The gap-like feature marked by the orange rectangle results from the phonon-assisted inelastic scattering in graphene. The Dirac point (conductance minimum point in STS) of the surrounding graphene is 0.24 eV below the Fermi level (n type doping), while it is 0.21 eV above the Fermi level in the graphene QDs (p type doping). The energy difference of the Dirac point indicates a potential barrier height of 0.45 eV of the QD with the surrounding n-type graphene.

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Figure 5. Thermoelectric imaging of hexagonal-like dark features in the SLG/Cu foil. (a) AFM topography of SLG on Cu foil without any structural disorders. (b) TEP mapping simultaneously obtained with ‘a’. Multiple dark spots appear. Scanning condition: ǻT=30 K, a contact force of 0.005 nN, and a pixel raster time of 20ms. (c) A magnification of the dark spot shown in ‘b’. (d) The TEP profile along the red-dashed line in ‘c’, indicating that the dark region has a ǻV variation of 0.47 mV. (e) A schematic model for the dark spot in ‘c’. Local defects on the Cu surface produce a shift in the Fermi level without making a resonant mode. (f) Energy band diagram for the schematic picture in ‘e’. 26


Coherent thermoelectric power from graphene quantum dots - Nano

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