Letter pubs.acs.org/NanoLett
Nanoscale Probing of Local Electrical Characteristics on MBE-Grown Bi2Te3 Surfaces under Ambient Conditions Rita J. Macedo,† Sara E. Harrison,‡ Tatiana S. Dorofeeva,† James S. Harris,‡ and Richard A. Kiehl*,† †
Department of Electrical and Computer Engineering, University of California Davis, Davis, California 95616, United States Department of Electrical Engineering, Stanford University, Stanford, California 94305, United States
‡
S Supporting Information *
ABSTRACT: The local electrical characteristics on the surface of MBE-grown Bi2Te3 are probed under ambient conditions by conductive atomic force microscopy. Nanoscale mapping reveals a 10−100× enhancement in current at step-edges compared to that on terraces. Analysis of the local current−voltage characteristics indicates that the transport mechanism is similar for step-edges and terraces. Comparison of the results with those for control samples shows that the current enhancement is not a measurement artifact but instead is due to local differences in electronic properties. The likelihood of various possible mechanisms is discussed. The absence of enhancement at the step-edges for graphite terraces is consistent with the intriguing possibility that spin−orbit coupling and topological effects play a significant role in the step-edge current enhancement in Bi2Te3. KEYWORDS: Bismuth telluride, topological insulators, van der Waals epitaxy, molecular beam epitaxy, atomic force microscopy
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and, possibly, surface reconstruction.21 Even when no native oxide is formed, however, the absorption of water, hydrocarbons, and other contaminates on surfaces exposed to air hinders characterization via ARPES and STM/STS.22 Thus, an alternative technique is needed for ambient conditions. Here we exploit conductive atomic force microscopy (CAFM) to characterize Bi2Te3 in air at room temperature. While C-AFM cannot provide the dispersion (E-k) or local density of states (LDOS) information of ARPES or STM/STS, it can provide a nanoscale mapping of topography and conductance and a detailed characterization of local electrical properties. The nanojunction formed between the metallic tip and sample in CAFM allows local current−voltage (I−V) measurements to be made over an extended voltage range, potentially allowing the identification of transport mechanisms. Moreover, C-AFM offers robustness to surface conditions because physical contact allows the tip to penetrate some of the surface contamination that would obscure characterization by ARPES or STM/STS. The topological order that is of keen interest in Bi2Te3 and related materials is in itself robust against surface conditions. Although chemisorption of O2 and reaction with atomic O on a Bi2Se3 surface upon exposure to air can produce changes in surface states and their spin properties, theory shows that the former process largely preserves the topological surface states and the latter process yields new topologically relevant states.23 This robustness of topological order in Bi2(Te,Se)3 samples exposed to ambient conditions has been confirmed experimentally by ARPES.24
esearch on three-dimensional (3D) topological insulators (TI’s) has attracted considerable attention in the scientific community due to fundamental interest in a new state of matter as well as its possible application in new spintronic or magnetoelectric devices.1,2 The first theoretical predictions3,4 have led to a flood of experimental work, which culminated in the groundbreaking discovery of topological insulator behavior in bismuth telluride (Bi2Te3).5,6 Bi2Te3 is among the most promising candidates for TI-based devices and is potentially compatible with conventional semiconductor growth and fabrication technologies. While progress has been made over the past few years in the growth and characterization of Bi2Te3 and other 3D TI thin films,7−12 many issues remain. Most studies of topological materials have been performed in situ under ultrahigh vacuum and at low temperatures on freshly cleaved or grown samples using angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), or scanning tunneling spectroscopy (STS).13−16 In order for these materials to be considered as building blocks for new devices, however, characterization of their electronic properties under ambient conditions will be required. An ideal (0001) Bi2Te3 surface should be inert because the Te surface layer of the quintuple layer is bonded covalently in the plane (no dangling bonds). The inertness of Bi2Te3 and Bi2Se3 surfaces has been confirmed by a number of studies, which show virtually no oxide formation after prolonged air exposure17 and negligible surface reactivity to O2, H2O, CO, and CO2.18,19 The fast formation and continuous growth of oxides found in some studies of Bi2Se3 nanoribbons and bulk crystals,20 however, indicates the important influence of sample quality and growth conditions on surface reactivity, which is affected by surface defect densities © XXXX American Chemical Society
Received: August 16, 2014 Revised: May 15, 2015
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DOI: 10.1021/acs.nanolett.5b00542 Nano Lett. XXXX, XXX, XXX−XXX
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Nano Letters Our C-AFM studies of current maps on Bi2Te3 terraces-step structures, combined with local I−V characteristics, reveal an enhancement in current of more that an order-of-magnitude at the step-edges between adjacent terraces. Analysis of the I−V data suggests that the transport mechanism is similar at stepedges and on terraces. Comparison of the results with those for control samples shows that the current enhancement at stepedges in Bi2Te3 is not a measurement artifact but rather is due to local differences in electronic properties. The absence of enhancement at the step-edges for graphite terraces is consistent with the possibility that spin−orbit coupling and topological effects play a significant role in the step-edge current enhancement in Bi 2Te 3 . Our findings provide complementary information about the electrical properties of topological insulators in the Bi2Te3 family under ambient conditions and motivate further studies into the underlying physical mechanisms of such materials and their potential for practical device applications. The Bi2Te3 thin films studied in this work were prepared by molecular beam epitaxy (MBE) using a two-temperature growth procedure on c-plane sapphire substrates.7 In this process, a low-temperature nucleation layer is first deposited to serve as a template for the high-temperature epitaxial film growth, yielding high crystalline quality Bi2Te3 thin films with a significant reduction in three-dimensional defect structures. The surface morphology of the 100 nm thick films examined in this study comprises micrometer-sized domains formed by wide concentric atomically flat terraces (see Supporting Information). Individual roughly triangular domains present a hillocklike surface morphology formed by a series of atomically smooth terraces with a concentric step structure.7 The average terrace width is approximately 170 nm and adjacent terraces are separated by a step height of 1.07 nm, which corresponds to the height of one quintuple layer in Bi2Te3. The atomic force microscope (AFM) tool employed in our study was a Park Systems XE-100. All the topographic-AFM and conductive-AFM images were obtained in contact mode under ambient conditions using a conductive gold NSC18/Cr− Au Si probe from Mikromasch. The nominal values of tip radius of curvature, resonant frequency, and spring constant were 50 nm, 75 kHz, and 3.5 N·m−1, respectively. The sample was mounted on a gold-plated slug and silver paint was used to make electrical contact between a small region near the edge of the Bi2Te3 film and the slug, thereby creating a side contact to the film. The conductive Cr−Au tip served as a local nanoscale contact to the film. The sample bias refers to the voltage applied to the side contact with respect to the tip. (See Supporting Information for additional instrumentation details.) Figure 1a and 1b show a typical topography image and its corresponding current map for an individual domain. The 1D line profiles obtained from the topographic and current images are shown in Figure 1c. Examination of this figure reveals that the high-current regions appear precisely where the tip makes a transition between one terrace and another, i.e., when the tip makes contact only to a step-edge (see Figure 1d). We refer to this region as the “transition region”. The enhanced current at the step-edges was studied in more detail by mapping currents for different bias voltages ranging from −0.5 to +0.5 V. The images were analyzed statistically to determine the average current values at the step-edges and on terraces for the various biases (see Supporting Information). The results in Figure 2 show that the current at the step-edges is more than an order-of-magnitude higher than on the terraces.
Figure 1. (a) AFM image (3 × 3 μm2) of an individual triangular domain and (b) corresponding C-AFM image (+0.5 V bias, 1 nN loading force, 1 Hz scan rate). (c) Topography and current 1D line profiles obtained from the locations marked in the corresponding 2D images. (d) Scheme describing the tip−sample interaction when the tip makes a transition between adjacent terraces. The expected contact areas on the terraces and at the step-edges are highlighted in RED for side and top views.
Figure 2. I−V characteristics obtained from current maps at fixed biases. (0.1 V steps, 1 nN load force, 1 Hz scan rate). Inset (a) shows the same data in logarithmic scale, revealing current at the steps-edges (open circles) of more than an order of magnitude higher than terraces (solid squares). Insets (b) and (c) show the 1 × 1 μm2 current map images acquired at −0.5 and +0.5 V, respectively. Note that the contrast at the step-edges inverts as the polarity of the applied bias is reversed, as expected.
In order to obtain more detailed information regarding the local electrical properties, the I−V characteristics were recorded B
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plots used to extract the barrier height πB and ideality factor n.25−28 For each data set, the average values for the top two curves and bottom two curves were taken to be representative of step-edges and terraces, respectively. A Richardson constant of 1.2 × 106 Am−2 K−2 and a correction factor of 0.5 were assumed and the effective electrical contact area was estimated by the method described by Sarid26 and taken to be 9.58 nm2 for a load force of 5 nN (see Supporting Information). Fitting was done for all sets of measurements and for both bias polarities and the results were averaged (see Supporting Information). For step-edges, the average and standard deviation for πB and n were 0.299 ± 0.03 eV and 8.260 ± 1.76, respectively. For terraces, the corresponding values were 0.351 ± 0.037 eV and 8.397 ± 1.89. Thus, within the TE model n is statistically the same for edge-steps and terraces while πB is slightly lower at the step-edges than on the terraces. Three factors suggest that in addition to a thermionic component the I−V behavior involves a tunneling process: the high values of n, the deviation from exponential dependence, and the near symmetry of the I−V characteristics. To examine this possibility, the data were fit with Fowler−Nordheim tunneling theory (FNT)29,30 in the high-bias regime. The example in Figure 4b shows that a linear dependence in ln[I(V)/V2] versus 1/V occurs at high V for both step-edges and terraces. The value of πB was calculated from the slope of the linear fit in the high bias regime using the same data treatment as described for the TE analysis. Because the nature of the effective tunneling barrier is not known, an oxide thickness of 1 nm and an effective mass of 0.1me, where me is the free electron mass, were assumed as a point of reference. The πB values extracted from the FNT model are statistically the same at the step-edges and on the terraces, 0.873 ± 0.314 and 0.875 ± 0.334 eV, respectively. Thus, while a more complete analysis of the I−V characteristics as a function of temperature would be helpful to clarify the details of the transport processes, our analysis indicates that current flows by a similar combination of thermionic and tunneling processes at the step-edges and on the terraces. (Note that both models give a lower barrier height for reverse bias than for forward bias, consistent with the asymmetry in Figure 3, see Supporting Information.) We can discriminate between artifacts31 and real behavior by considering some details of the results. The high-current region and transition region shown in Figure 1c are colocalized and are 19 nm in width. Although the step-edge for a single quintuple layer of Bi2Te332 should be atomically abrupt, a finite transition region is expected in the AFM images due to tip curvature. From simple geometric considerations (see Supporting Information), the width of the transition region (where the tip only contacts the step-edge) would be 10 nm for a 1 nm step and spherical tip with a 50 nm radius-of-curvature. The larger measured value can be easily accounted for by a larger effective radius-of-curvature near the tip apex due to deviations from a perfectly spherical shape. Thus, the apparent width of the transition and high current regions is an expected artifact of the measurement. An asymmetry in the degree of step-edge current enhancement is seen in the current map in Figure 1b. Such asymmetry is typical of C-AFM images acquired for one scan-direction due to the dynamics of the AFM feedback loop.33 Feedback delay leads to larger tracking errors at the edges than on the terraces, which results in increased force at rising steps and decreased force at falling steps. The greater enhancement on the left-half
by sweeping the bias from 1 to −1 V at fixed positions on the sample. Different points on the sample were targeted, including positions on the terraces and at the step-edges. While it was not possible to know the exact location of the tip because of thermal drift, the current maps allow us to unambiguously associate the curves having the highest currents with positions at the step-edges and the remaining curves with positions on the terraces (see inset (a) of Figure 3). Figure 3 shows a
Figure 3. I−V characteristics obtained by sweeping bias voltage at fixed locations (5 nN load force, tip−sample contact area of ∼9.58 nm2). Inset (a): correlation of this data with current maps. Inset (b): linear representation of I−V characteristics. Inset (c): illustration of the single point method.
representative set of I−V characteristics obtained from nine different positions on the sample. It can be seen from Figure 3 that the I−V characteristics are highly symmetric and exponential at high biases for both polarities. The range of current at a given bias voltage over the set of I−V curves is again found to be greater than one order-of-magnitude. The I− V characteristics were highly reproducible and insensitive to tip loading force (see Supporting Information). The I−V characteristics were fit to two different electron transport models to gain insight into the electrical behavior. Taking into consideration the exponential behavior at high bias, thermionic emission (TE) theory was used for one model. Figure 4a shows an example of the linear fit to Ln(I) versus V
Figure 4. Example of data treatment for study of the transport mechanism. This data was extracted from the set of measurements shown in Figure 3. (a) ln(I) versus V curves for fitting of TE and (b) ln(I/V2) vs 1/V curves for fitting of Fowler−Nordheim tunneling (FNT) model. Plots (a,b) show only the two highest current curves (attributed to step-edges) and the two lowest current curves (attributed to terraces). Linear fits used to extract the transport parameters are shown. For simplicity, only the negative bias is shown here. An identical analysis was performed for positive bias and the values for both polarities were then averaged (see Supporting Information). C
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Nano Letters of Figure 1b, which was scanned left-to-right, and observed on the right-half of images acquired in the opposite scan direction (see Supporting Information, Figure 5S) are explained by the greater force on rising step-edges, which could increase contact area or conductance. However, we found that this asymmetry could be eliminated by optimization of the scanning parameters. (Details on the effects of scanning direction and parameters are given in the Supporting Information.) Moreover, the feedback dynamics are in fact useful for investigating whether lateral forces between the tip and sample are responsible for the observed current enhancement due to transient or permanent changes in the sample during scanning. Both possibilities are discussed below. One question is whether the current enhancement could be caused by a physical change, such as local removal of oxides or surface contaminates, at the step-edges produced by the tipprobe interaction during scanning. Two observations show that the current enhancement is not caused by a physical change in the sample at step-edges during scanning. First, due to feedback dynamics the tip−substrate interaction is weaker at falling steps than on terraces, whereas we observe enhanced currents at rising, as well as falling step-edges. Second, in repeated imaging of the same terraces, the orientation of the asymmetry in the current map was not affected by rotation of the sample by 90°, that is, the brighter regions did not rotate (see Supporting Information). If the enhanced current regions had been created during repeated scanning in one orientation, by physical changes of the sample, those regions would have rotated with the sample. In AFM, the surface morphology and the tip geometry are convoluted,33,34 and this can produce artifacts in the current map due to changes in the contact geometry and area as the tip probes different contours along the surface. Nonuniformities in the conductive coating can also produce artifacts due to changes in the point-of-contact to the surface during a scan. To examine these possibilities, a control sample comprised of 20 nm Fe3O4 nanoparticles (NPs) deposited on a graphene/SiO2/ Si substrate was examined. Because the NP radius is comparable to the tip radius-of-curvature, the current map can be used to evaluate the uniformity of the tip conductance over a wide range of positions both near to and far from the apex of the tip. Figure 5a,b shows images for NP made using the same tips as used for imaging a Bi2Te3 sample. A very small (∼20%) increase in current is seen along the edges of the NPs. As illustrated in the inset of Figure 5 a, when a spherical particle is imaged by a tip of comparable radius-of-curvature, a slight increase in the contact area is expected near the edges of the NPs due to the nonspherical shape of the tip far from the apex. Thus, the slight enhancement in current at the NP edges in Figure 5b can be explained by a geometric artifact. It is important to note, however, that this slight enhancement is entirely negligible compared to that for the step-edges on Bi2Te3. Regarding coating nonuniformities, any difference between the conductance at the apex of the tip and nearby points would be revealed in the current map as a difference in contrast in a small region at the center of each NP. Because this is not seen in Figure 5b, we can conclude that the step-edge current enhancement in Bi2Te3 is not the result of reduced conductance at apex of the probe tip or other tip-related artifacts. Geometric artifacts due to changes in contact area would also be expected to be small at abrupt step-edges. Elastic deformation of the tip and sample during contact results in a
Figure 5. AFM image of Fe3O4 NPs on graphene (a) and corresponding current map (b). The inset on (a) describes the tip− sample interaction for the case of spherical particles imaged by a tip of comparable radius of curvature. AFM image of an HOPG sample (c) and corresponding current map (d). The insets on (b−d) show the 1D profiles along the lines represented in the images.
circular contact on terraces and a line contact (narrow rectangle) at step-edges, as depicted in Figure 1d. Typically the circular terrace contact is expected to be somewhat larger than the linear edge contact; in any case, the two areas should be approximately the same. Thus, the 10−100× higher current at step-edges cannot be explained by differences in contact area. In the case of an abrupt step-edge, the tip makes contact only along the line of the step-edge in the transition region, compared with contact over a circular area on the terrace surface (see Figure 1d). Thus, a geometric artifact would decrease the contact area and the current in the transition region, the opposite to what is observed for step-edges on Bi2Te3. However, since tip−sample interactions are complicated by a combination of geometric, force, and elastic responses, further studies were carried out for a control sample with abrupt step-edges. Being a 2D van der Waals material comprised of graphene layers with abrupt terrace steps, HOPG is very similar morphologically to Bi2Te3. In comparisons of HOPG and Bi2Te3 samples, the HOPG I−V characteristics were found to be nearly linear with current levels approximately 6 orders-ofmagnitude higher than for Bi2Te3 (see Supporting Information). We examined steps of approximately 0.25 and 1.0 nm on HOPG, which correspond to the step for a graphene monolayer and for a multilayer comparable in height to the terrace step on Bi2Te3, respectively. Figure 5c,d shows the topography and current maps for a monolayer step on HOPG. The current increases by only 17% at the step-edge in Figure 5c, which is comparable to what was found for 1.0 nm step edges (25%) and is negligible compared to the 10−100× increase observed at Bi2Te3 step-edges. Thus, we can conclude that the observed current enhancement at step-edges in Bi2Te3 is not a measurement artifact, but rather is the result of differences between the local electronic transport properties at the step-edges and on the terraces. D
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from the step-edges should strongly increase the local conductance. Furthermore, this conduction channel is expected to be highly efficient because the topological surface states are “protected” by time-reversal symmetry with suppressed back scattering. This scenario is supported by a variety of experimental and theoretical studies that have revealed novel transport phenomena at step-edges in Bi2Te3. Using low-temperature STM and STS, Zhang et al.14 observed voltage-dependent interference fringes at step edges, which confirmed the prediction of suppressed backscattering. Seo et al.39 showed that transmission through terrace stepedges occurs with high probability for the topological surface states on antimony, which is in contrast to the case for nontopological surface states of common metals. In an STM study of the DOS near a step-edge in Bi2Te3, Alpichshev et al.15 identified a 1D bound state in the bulk gap that is bound to the step edge. In a theoretical study of states on edges between surfaces in 3D topological insulators, Deb et al.40 identified localized states that may propagate along step-edges, thereby providing an additional current path. The possible roles of a number of nontopological effects also should be considered. In addition to the effect of extended orbitals at step-edges on coupling, these dangling bonds could act as edge defects, which could shift the Fermi-level causing an increase in the local density of states (LDOS), thereby increasing the step-edge conductance. This could have a significant affect in insulating material where the Fermi-level lies in the bulk gap. In highly doped material, bulk conduction or valence band states at the Fermi level could also contribute to tunneling current. When the tip is on a terrace, the tunneling is mostly perpendicular to the surface and the in-plane k values for wave function matching are restricted to near zero, resulting in a small available phase-space and a small effective conductance. When the tip is at a step-edge, a larger range of in-plane k values are involved and the available phase-space is much larger. Thus, as for metallic surface states, a higher conductance would also be expected at step-edges in the case of bulk states. Structural defects (e.g., vacancies and antisite defects) may accumulate or be relieved at the step-edges. An accumulation of defects could effectively increase the doping at the step-edge, thereby increasing the local conductivity. Also, crystal strain could be different at the step-edges due to either (i) strainrelaxation at the edges or (ii) increased strain during scanning caused by the lateral force from the AFM tip. Differences in strain could alter the band structure and piezoelectric effects, either of which could alter conductivity. We believe that strain at step-edges in Bi2Te3 would be small, however, because of the weak van der Waals bonding in this material. We also believe that it is unlikely that lateral tip forces play a significant role since we observe current enhancement even for fixed-position measurements, where the tip is motionless. The formation of a surface oxide that is thinner at the step-edges than on terraces might also explain the current enhancement. This seems unlikely, however, because one expects the step-edges to be more reactive than the terraces due to the presence of dangling bonds at the step-edges. Thus, an oxide would be expected to be thicker, not thinner, at the more reactive step-edges. We have used C-AFM to probe the local electrical characteristics of MBE-grown Bi2Te3 under ambient conditions as a complementary technique for basic surface science studies and as a realistic approach for baseline characterization of topological insulators for device applications. We find a 10−
HOPG and Bi2Te3 are very similar physically, having similar topographies (terraces) and elastic moduli (∼40 GPa), however, they are very different electronically. HOPG has weak spin−orbit coupling and is a conductor, whereas Bi2Te3 has strong spin−orbit coupling and is a topological insulator. The orbitals relevant to coupling to an AFM tip are also very different for these materials. Experimentally, the conductances measured for HOPG, graphene monolayer, and Bi2Te3 samples were also very different. These differences can shed light on the possible mechanisms underlying the observed current enhancement at step-edges. HOPG consists of van der Waals coupled graphene layers and has a 3D semimetallic character.35 Thus, tip−sample coupling is very strong (similar to coupling to a metal) and one should expect a conductance near the quantum of conductance Go of 0.77 × 10−4 S. For HOPG, we observe an ohmic I−V characteristic with a conductance GHOPG of about 10−4 S (see Supporting Information, Figure S4). This agreement of GHOPG with Go helps to confirm the validity of our measurement technique. The coupling of the tip to a graphene monolayer is expected to be weaker than to HOPG due to mismatch between the orbitals in the AFM tip and this 2D material. In graphene, sp2 hybridized orbitals are responsible for bonding in the x−y plane, while the remaining 2p orbitals extend perpendicular to the atomic plane, thereby providing coupling to the tip. However, this coupling is from a 1D z-channel to a 2D x−ychannel, and the orbital mismatch results in weak coupling. Experimentally, we observe a 5 orders-of-magnitude lower conductance for graphene GGR than GHOPG. Since the graphene and HOPG surfaces are chemically similar and free of oxide, this shows that a 5 orders-of-magnitude reduction in conductance can be accounted for by orbital mismatch alone. The coupling of the tip to Bi2Te3 is expected to be even weaker than to graphene. Similar to the case for Bi2Se3,36 the topological surface states in Bi2Te3 are mostly confined within the first quintuple layer. These orbitals have px and py character but unlike the case for graphene do not extend perpendicular to the atomic surface layer,37 and the coupling should therefore be weak. The bulk states in Bi2Te3 are localized several quintuple layers below the surface. Because of this and surface depletion, the coupling to bulk states also should be weak. Experimentally, we observe a conductance GBiTe for Bi2Te3 that is about 1/10 of GGR (see Supporting Information, Figure S4), which can reasonably be accounted for by the increased orbital mismatch. From the above discussion, we see that the low values of conductance observed on Bi2Te3 terraces can be accounted for by orbital mismatch without the need to invoke potential barriers due to surface oxides or contaminants. Indeed, C-AFM studies of Bi2Te3Se surfaces exposed to atmosphere showed negligible conductance change after in situ cleaning at UHV,38 showing that a surface oxide (if present) had little effect on current measured by C-AFM for this material. We also presented evidence that the presence of surface oxides or contaminates would not explain our detailed results on current enhancement at step-edges. Our observation of current enhancement at step-edges in Bi2Te3 (strong spin− orbit coupling) and not at step-edges in HOPG (weak spin− orbit coupling) is consistent, however, with the interesting possibility that spin−orbit coupling and topological effects play a significant role in the enhancement at step-edges for Bi2Te3. An enhanced coupling to topological surface states at stepedges in Bi2Te3 due to modified orbitals that extend outward E
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100× enhancement in current at step-edges compared to that on terrace surfaces. Comparison of the results with those for various control samples shows that the current enhancement is not a measurement artifact but instead is due to local differences in electronic properties. The absence of current enhancement found at the step-edges for graphite terraces is consistent with the intriguing possibility that spin−orbit coupling and topological effects play a significant role in the enhancement observed for Bi2Te3. These results motivate further studies of the local electrical characteristics for topological insulators under ambient conditions as essential background for understanding their basic electronic properties and potential device applications. Two particularly interesting extensions of this work would be to examine the effect of shifting the Fermi-level by electrical gating and the effect of lifting the topological protection by the introduction of a magnetic field.
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ASSOCIATED CONTENT
S Supporting Information *
Surface morphology, instrumentation, statistical analysis of current maps, reproducibility of data and effect of tip load force, estimation of effective contact area, extraction of barrier height and ideality factor, calculation of transition region width, current map of HOPG 0.74 nm-step, I−V characteristics for Bi2Te3, HOPG, and graphene, and effects of scanning direction, scanning parameters, and sample orientation on the AFM images. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.nanolett.5b00542.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS R.A.K. and R.J.M. thank Professor Tai-Chang Chiang (UIUC) and Dr. Byong Kim (Park Systems Inc) for their insightful comments on these results regarding physical properties of Bi 2 Te 3 surfaces and physical interactions in C-AFM, respectively. The authors would also like to thank Yijie Huo and Shuang Li for contributions to the material growth and Samuel B. Ravani for his contribution to data analysis. S.E.H. and J.S.H would like to acknowledge funding support from DARPA’s MesoDynamic Architectures Program (No. N6600111-1-4105)
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DOI: 10.1021/acs.nanolett.5b00542 Nano Lett. XXXX, XXX, XXX−XXX
