Silicon carbide stacking-order-induced doping variation in epitaxial graphene

Generally, it is supposed that the Fermi level in epitaxial graphene is controlled by two effects: p-type polarization doping induced by the bulk of the hexagonal SiC(0001) substrate and overcompensation by donor-like states related to the buffer layer. In this work, we evidence that this effect is also related to the specific underlying SiC terrace. We fabricated a periodic sequence of non-identical SiC terraces, which are unambiguously attributed to specific SiC surface terminations. A clear correlation between the SiC termination and the electronic graphene properties is experimentally observed and confirmed by various complementary surface-sensitive methods. We attribute this correlation to a proximity effect of the SiC termination-dependent polarization doping on the overlying graphene layer. Our findings open a new approach for a nano-scale doping-engineering by self-patterning of epitaxial graphene and other 2D layers on dielectric polar substrates.


Introduction
The growth of epitaxial graphene on large-scale silicon carbide (SiC) substrates enables the fabrication of electronic devices for a wide range of technological applications in an industrial fabrication environment. [1][2][3] The role of SiC exceeds that of a simple carrier of the graphene sheet as it influences the basic electronic properties of the graphene in different ways and thus can be used for further modification of graphene's electronic properties. The most commonly used SiC substrates are of the hexagonal 4H and 6H polytypes, which exhibit a spontaneous polarization induced by the hexagonal stacking sequences in the SiC unit cell. The spontaneous polarization of the hexagonal SiC polytypes leads to a phenomenon called polarization doping, i.e., a p-type doping of the order of 6 -9 × 10 12 cm −2 in so-called quasi free-standing graphene on hydrogen saturated SiC(0001). [4] On the other hand, epitaxial graphene residing on the buffer layer shows an n-type conductivity with a charge carrier density of the order of 10 13 cm −2 . This is attributed to an overcompensation of the polarization doping by electron transfer from a donor-like buffer layer and interface states to the graphene layer. [4,5] Superimposed on these fundamental and spatially homogenous effects, the interplay between the hexagonal SiC and atop carbon layer is a source of various other intriguing phenomena, e.g., step-induced extrinsic resistance anisotropy in graphene [6][7][8][9], dislocation boundary domains [10], room-temperature strain-induced quantum Hall phase [11] and ballistic transport at SiC sidewalls [12], the Stark effect [13] and quantum photonics in SiC defect sites and color centers [14], as well as offering an excellent platform for growing other lowdimensional materials [15][16][17]. In general, the graphene properties on the SiC terraces are assumed to be uniform. These terraces, considering the stacking order in the unit cell of hexagonal SiC, result in inequivalent surface "terminations." Given that, some doubt is raised because theoretical investigations estimate a certain dependence of the doping on the stacking sequence and surface terminations of 4H-and 6H-SiC. [18][19][20][21][22] Moreover, a very recent nanoscale transport study reported up to a 270% variation (at low temperature) of the sheet resistivity for epitaxial monolayer graphene on two different terminated 6H-SiC terraces. [23] In this paper, we experimentally show that the stacking terminations of the hexagonal SiC substrate have a biasing effect on the surface potential leading into a work function variation and thus a shift of the doping level of the overlying epitaxial monolayer graphene. Using the so-called polymer-assisted sublimation growth (PASG) technique, monolayer graphene on identical and non-identical SiC terraces was fabricated. In our study, various surface-sensitive measurement techniques, namely atomic force microscopy (AFM), scanning tunneling microscopy (STM), low-energy electron microscopy (LEEM), kelvin-probe force microscopy (KPFM), and X-ray photoemission electron microscopy (XPEEM) indicate different electronic properties of graphene on inequivalent SiC surface terraces types in association with their cubic and hexagonality nature. These SiC terraces can be clearly assigned to the specific stacking terminations within the framework of an extended SiC step retraction model.

AFM analysis of graphene and buffer layers on identical and non-identical 6H-SiC terraces
The epitaxial buffer and graphene layers in this work were grown on semi-insulating 6H-SiC samples with a nominal miscut of about −0.06° toward [1100] (from II−VI Inc.). Epitaxial growth was carried out in a horizontal inductively heated furnace. [24] The buffer layer and graphene samples were grown by the PASG technique in an argon atmosphere (~900 mbar) at 1400 °C and 1750 °C, respectively. [8,9,25] The control of the surface morphology was attained by taking into account the influence of Ar flux during the sublimation growth. [9] Figure 1(a-d) and (g-j) show AFM images of the epitaxial monolayer graphene and buffer layer, respectively, with two types of surface morphologies. The origin of the different surface morphology will be explained in the next section. The AFM topography images of the graphene samples in Figure 1a and b show that one sample exhibits regular ~0.75 nm step heights while the other one displays a step pattern consisting of alternating ~0.25 nm and ~0.5 nm high steps. The phase images of these samples in Figure 1c and d show a very interesting behavior. For the ~0.75 nm stepped surfaces, the same phase is observed on all terraces.
Only step edges appear as narrow regions with increased phase. On the other hand, ~0.25/~0.5 nm stepped surface clearly shows an alternating phase (Figure 1d), which changes from one terrace to the next. As for the other sample, step edges appear as narrow regions with increased phase. The observation of two different phase values indicates different material properties of the graphene layer on neighboring SiC terraces. Importantly, this phase contrast is not caused by a different number of graphene layers. The integrated Raman spectra (areal scan over 20 × 20 µm 2 ) in Figure 1e and f reveal a similar spectrum for both samples and a typical 2D-peak (at ~2724 cm −1 and full-width-half-maximum of about 33 cm −1 ) which proves that both samples are uniformly covered with monolayer graphene. [9,26,27] Similar contrast was also seen in the scanning electron microscopy of the sample with sequential terrace-steps. [28] The AFM investigation of the buffer layer samples (Figure 1g-j) leads to a very similar result.
Again, the regular ~0.75 nm stepped SiC terraces (see Figure 1i) show no phase contrast and only for the binary ~0.25/~0.5 nm stepped terraces an alternating AFM phase contrast is observed (see Figure 1j). The integrated Raman spectra in Figure 1k and l show a broad buffer layer related vibrational band, which indicates a homogenous buffer layer coverage. [29] The agreement of the phase contrast of graphene and the buffer layer samples for the same substrate step structure clearly points to a substrate related effect changing the properties of the overlying layer, be it the epitaxial graphene or the buffer layer. An intrinsic effect of the graphene layer itself thus can be ruled out. In AFM experiments, the phase image contrast arises from local variations of the energy dissipation in the tip-surface interaction, which results in damping and shift of the tip's oscillation frequency giving information about the < 4 > chemical/mechanical/electrical heterogeneity of a surface. [30] Thus, the observed phase contrast on non-identical terraces is associated with a change of the surface properties originating from the different SiC stacking terminations of the corresponding terraces below. Therefore, in the following, the formation and nature of the SiC surface terraces are analyzed.

Step retraction model of 6H-SiC(0001)
The formation of the SiC terraces during graphene growth can be understood in the framework of the SiC step retraction model applied to the 6H polytype SiC(0001) substrate. Figure 2a illustrates the unit cell of 6H-SiC consisting of 6 Si−C bilayers called A, B, C, A, C, B (from bottom to top). For our investigation, we focus on the 6 resulting Si-terminated surface-terraces which differ in three inequivalent stacking sequences of the underlying Si-C bilayers, i.e., S1, S2 and S3, and another three stacking sequences, S1*, S2*, S3*, which are equivalent to the first ones but rotated by 60°, see Figure 3b. [31] The number gives the number of SiC bilayers between the surface and the first hexagonal stacking arrangement. For simplicity, we name them S1, S2, and S3 if the rotation can be neglected. The eclipsed and staggered orientation of subsequent Si−C tetrahedra are called hexagonal (h) and cubic (k), respectively, which leads to discrete h, k, and k stacking orders of A, B, and C. In a more detailed model, one can assign to each atomic layer a hexagonal or cubic orientation, which is sketched in Figure 2a. [14] For the on-bonds in axial configuration ([0001] direction), this results in hh, kk, and kk stacking for the layers A, B, and C, respectively. The off-bonds (basal configuration) are described by kk (for S2) but also by mixed hk (for S3) and kh (for S1) stacking orders. The hexagonality of each surface terrace can be considered as the joint hexagonality of the corresponding on-and off-bonds.
The schematic representation of the terrace structure with single Si−C steps (1L) of ~0.25 nm, in Figure 2b and c, can be regarded as the initial surface of the low-miscut angle substrates used here. During graphene growth at high temperatures, a restructuring of the SiC surface takes place which can be described by retraction of individual Si-C bilayers with different velocity in a so-called step retraction model. [32][33][34] The step retraction is driven by the minimization of the surface energies, which depend on the surface hexagonality of the individual terraces. [22,34] This step retraction velocity is indicated by the length of the horizontal arrows in Figure 2b. The high retraction velocity of the S1 surface can be attributed to the strongest hexagonality (hh on-bond) of this layer in agreement with refs. [32,33]. Thus, the corresponding S1 surface disappears at first. S2 and S3 remain, which results in a periodically stepped surfaces with ~0.25 nm (1L) and ~0.5 nm (2L) step-heights, as observed in the AFM image in Figure 1b and h. This situation is sketched as an intermediate state in Figure 2c. From this model, we can clearly assign the S3 terrace being above a 1L step and an S2 terrace above a 2L step. It is further assumed that S2 is the most stable surface because < 5 > of its least hexagonality (kk on-bond and kk off-bond) and, therefore, the width of the S3 terrace (kk on-bond but hk off-bond) is decreasing faster than S2, which agrees with the model in ref. [33,34] but not ref. [32]. The width of the initially wider S3 terrace (see buffer layer AFM image in Figure 1h and ref. [9]) decreases, and for advanced step retraction the S3 terraces become narrower than S2. This situation is found for all graphene samples, see Figure 1b and in refs. [8,9,25]. (Such a pattern could not be primarily formed if S2 would retract faster than S3.) Finally, only the stable S2 terraces remain with step heights of ~0.75 nm (3L), sketched as the final state in Figure 2c. This situation is observed in the AFM images in Figure 1a and g.
The preparation of a ~0.25/~0.5 nm stepped surface with alternating S2 and S3 terraces of nearly 100% efficiency is a specific advantage of the PASG method. [8] The fast formation of the buffer layer by the additional polymer-related carbon supply stabilizes the SiC surface and reduces the step bunching velocity. As a result, the terrace structure can be "frozen in" at the intermediate state with S2 and S3 terraces before the final state with S2 surfaces only, is reached. [25,28]

Assignment of the SiC terminations below the graphene layer
A bright-field (BF) LEEM image of the ~0.25/~0.5 nm (1L/2 L) stepped graphene sample is displayed in Figure 3a. In the upper part of this image, a regular contrast pattern of alternating narrower brighter and wider darker stripes is observed. From the similarity to the AFM pattern, the BF-LEEM stripes are identified as the terraces S2 (wide) and S3 (narrow). Note that the step edges between the terraces lead to the thin dark lines in Figure 3a. From the correlation between terrace width and step height (narrower S3 being above a 1L and wider S2 being above 2L step), we can ascribe the corresponding step-heights to the boundaries between areas of different brightness, which is visualized by the top blue profile in Figure 3a. The underlying regular SiC step structure is sketched in part (i) of Figure 3e (For clarity the covalently bonded buffer layer and the overlying graphene layer are left out in this sketch). The bright-field image depicts the reflected intensity of the 0 th order low-energy electron diffraction (LEED) spot. The usual attribution of the BF contrast to a graphene thickness variation [35,36] is not valid here since the sample is unambiguously covered only with monolayer graphene.
As will be discussed further below, the different brightness in the BF-LEEM images can be related to a variation of the surface potential, which is induced by the stacking of the SiC crystal underneath.
Next to the very regular S2/S3 terrace pattern in the upper part of this BF-LEEM image, there also irregular terrace configurations are observed in the lower part of  For a test of the surface structure model, also the dark field (DF) LEEM image was recorded using the moiré diffraction spot marked in Figure 3d. The moiré diffraction spots arise from multiple scattering at the graphene and SiC lattices and thus carry information about the SiC lattice orientation. The resulting DF-LEEM image is shown in Figure 3b. It also exhibits a sequential binary contrast pattern, but interestingly, the width of both stripes is wider and not congruent with the stripes observed in the corresponding BF image, Figure 3a. For the regular stepped upper part of the LEEM images (see the line (i) in Figure 3a and b), we can deduce that two terraces (one bright and one dark stripe in BF) comprise one stripe in the DF image.
This situation is sketched in Figure 3c. The origin of the DF contrast is the 60° rotation between the equivalent surface terminations Sn/Sn*, which causes a 60° rotation of the respective threefold diffraction spots patterns (see Figure 3d) of the terrace, which is sketched as green and purple areas in Figure 3b. Thus, when crossing a step from S to an S* (or vice versa) terminated terrace (S2-S3*, S2*-S3, S2*-S2, S3*-S3) the LEED pattern is rotated by 60° and a change of the DF contrast appears. On the other hand, no contrast inversion takes place when crossing a step from S3 to S2 or from S3* to S2*, since the direction of the underlying SiC is preserved. Using this interpretation also the irregular regions of the LEEM image can be explained, which is sketched in Figure 3e for the lines (ii) and (iii). With the described model, the different contrast patterns of the dark-and bright-field LEEM images complement each other and result in a consistent view of the underlying SiC terrace structure. With the input of the AFM results and the presented step retraction model, an unambiguous assignment of the step heights is possible, as are labeled in Figure 3a-b.

Verification of the SiC terrace model by scanning tunneling microscopy
A confirmation of the presented surface terrace model and a visualization of the SiC surface crystal orientation is provided by a low-temperature scanning tunneling microscopy (STM) investigation of the graphene sample.  LEEM results, which showed that for the S to S* crossings the underlying SiC surfaces are accompanied by a 60° rotation, but the crystal orientation is retained for all S* to S* or S to S crossings. The tight correlation of the (6 × 6) and the (6√3 × 6√3)R30° diamond rotations across the terrace steps show very instructively that the buffer layer strictly follows the rotation of the underlying SiC lattice.

Surface potential and work function measurements of graphene on non-identical SiC terminations
So far, AFM phase images reveal that the surface properties of graphene monolayers are different depending on the stacking termination of the underlying SiC terrace, which is in good agreement with the observed reflectivity contrast in the BF-LEEM images. In this section, we use additional methods to quantify the energy difference between the terraces and we discuss possible origins.   − eVS3)). [36,45] The KPFM map in Figure 5b also shows the elevated surface potential of bilayer graphene (BLG) spots (red areas), which have formed around a substrate defect on an S3 terrace. The homogenous potential of the bilayer graphene is also used to measure the relative difference to the monolayer graphene on both types of terraces. The local potential variation along the line scans correlated with an S2 and S3 terrace (magenta and green line in Figure 5b) is measured and the values are plotted in the histogram in Figure 5c. A clear difference between the S2 and the S3 related potential is observed with a value of VS2 − VS3 = 12 ±2 mV in reasonable agreement with the previous value from areal integration. The potential difference between monolayer and bilayer graphene is much larger with a value of about 60 mV, which is consistent with literature data but smaller than the reported values for vacuum measurements. [43][44][45][46][47] It is known that the absolute surface potential value is reduced by moisture and atmospheric adsorbates on the surface as well as intrinsic limitations of AM-KPFM and thus makes it difficult to precisely assess the surface potential difference. [44,45,48,49] It is worthwhile to mention that a potential difference of 10-20 meV for monolayer graphene on different terraces can also be seen in AM-KPFM (in air) measurement in ref. [43], which was not discussed.
As a second approach, low-energy electron reflectivity (LEEM-IV) measurements are used to deduce the graphene specific energy from the energy dispersion of the reflected electron beam in BF µ-LEED geometry. [50] The LEEM-IV measurements in Figure 6a were performed in vacuum with thermally cleaned surfaces on two neighboring terraces, S2 and S3. All LEEM-IV spectra show one prominent minimum, which is the signature of monolayer graphene in agreement with the Raman measurements in Figure 1f. [51,52]  shows an identical contrast pattern (compare the upper part of Figure 3a). This shows that next to the reflected intensity of BF-LEEM, also the energy of the minimum is correlated with the underlying SiC surface termination.
For the neighboring terraces S2 and S3, an energy difference of (ES3 − ES2) of (60 ±10) meV is estimated from the minimum energy histogram in the inset of Figure 6b, which indicates a < 9 > distinct difference in the graphene properties on both terraces. It worthwhile to mention that nearly the same value was measured for the graphene on 4H-SiC with non-identical terraces, however this polytype does not show a sequential pattern of terraces like 6H-SiC. [8] Although, in an early publication, the minimum energy was related to the graphene work function under the assumption that the reflectivity spectrum is related to discrete energy levels in the conduction band along the Γ-Α direction of the graphene band structure, [52,53] a recent study suggests, that the graphene interlayer bands play the decisive role. Following this model, the minimum position depends on the distance between the buffer and graphene layer and the corresponding correlation-exchange potential. [50,54] To explain the systematic shift of the LEEM-IV minima, at least one or both parameters should be different for graphene on S2 and S3 terraces. Since High-resolution STM measurements [23] on comparable 1L/2L stepped PASG graphene samples revealed fluctuating step heights variations (with smaller as well as larger on both 1L and 2L steps), thus systematic step heights differences can be excluded.
This suggests a considerable difference in the correlation-exchange potential for both terraces, which is sensitive to the different charge densities. More detailed model calculations are necessary to verify this assumption.
As the third complementary method, X-ray photoemission electron microscopy (XPEEM) was applied, which directly visualizes the work function variation on the surface. KPFM and XPEEM reveal in good agreement a lower work function for monolayer graphene on S2 compared to S3 terraces, and also the LEEM-IV result points to this direction. A reliable < 10 > value for energy difference of ~10 meV was measured by KPFM, knowing that this value might depend on the environmental conditions. [49] The strong XPEEM contrast points to a higher energy difference, but beam damage effects prevent a more precise estimate of the energy difference. More detailed studies are necessary to clarify the absolute value of the energy difference.
Up to now, other experimental results are lacking. The local measurements of the sheet resistivity by high-resolution scanning-tunneling potentiometry (STP) on similar 1L/2L stepped samples (thermally cleaned) have indicated a difference of the average graphene sheet resistance by ~14% at room temperature and ~270% at low temperature (8 K) on both terraces S2 and S3. [23] For terraces connected by a 3L step, a smaller variation of < 3% is measured. [4] A specific terrace related polarization effect can be deduced from ab-initio pseudo charge calculations, which show a different valence band charge density for cubic and hexagonal SiC layers in the 6H polytype and a different charge density depending on the distance to the next underlying hexagonal layer. [20,21] In a recent publication, the total polarization doping effect of SiC surface and bulk was investigated by standard density functional theory calculations which show a SiC surface termination dependent doping variation of 2 × 10 12 cm −2 for freestanding monolayer graphene. [18] However, the corresponding shift of the Dirac point of < 11 > This discussion shows that the assumption of a SiC stacking termination dependent polarization doping can explain the presented experimental results. Other effects, e.g., an influence of terrace dependent stress is less probable by the observation of strong contrast patterns also in more relaxed free-standing mono and bilayer graphene. [9] [to be published] A partial influence of different defects at both SiC terraces types can, however, not be ruled out. An example of a possible defect state in hexagonal SiC is the basal vacancy/divacancy, which can occur in a quasi-cubic or quasi-hexagonal position (shown in Figure 2a) with an energy difference of 0.03 eV. [56] Both quasi-positions are typical for the cubic S2 (0% hexagonality) and S3 (50% hexagonality) surfaces. To which extend such an effect plays a role requires further studies.  RMA15-0024). We thank the support DFG Project Te386/12-1.

Summary and conclusions
We also acknowledge funding from the European Commission Graphene Flagship Core2 (grant agreement 785219).

Experimental section
Sample preparation. Samples in this study were grown on semi-insulating 6H-SiC(0001) specimens (5 × 10 mm 2 ) with a nominal miscut of about −0.06° toward [1100]. The SiC samples were first cleaned with acetone/ isopropanol in an ultrasonic-bath (USB) (15 min, 40 °C). The PASG method was applied using a so-called liquid-phase deposition (LPD) in a way that the samples were immersed into a mixture of AZ5214E polymer with isopropanol (25ml/ 5ml) and introduced to the USB (15 min, 40 °C). The specimens were subsequently rinsed with isopropanol (30 sec) before being spin-dried. [25,28] This results in nano-sized polymer adsorbates on the sample helping the growth uniformity. The buffer layer and graphene samples were grown in an argon atmosphere (~900 mbar) at 1400 °C and 1750 °C, respectively. [8,9,25] The control of the surface morphology was attained by several optimizations of growth parameters, including the influence of Ar flow-rate during the sublimation growth. [9] Raman spectroscopy. Confocal micro-Raman mappings were performed at ambient conditions with a LabRAM Aramis Raman spectrometer (Horiba) equipped with a 600 mm −1 grooves holographic grating, a frequency-doubled Nd: yttrium-aluminum-garnet laser emitting at 532 nm (EL = 2.33 eV), and a 100× (NA 0.9) objective to focus the excitation laser onto the surface of the samples. Surface Raman mapping images were captured over (20 × 20) µm 2 areas in backscattering mode using a piezo-driven XY-stage (PI) and a scanning step size of 0.1 µm.
Atomic force microscopy/ kelvin probe force microscopy. The AFM investigations were performed using two AFM setups: (i) the NANOStation AFM equipped with the SSS-NCLR silicon tips fabricated by "Nanosensors TM ," and (ii) the NanoWizard AFM system made by JPK instruments AG. The latter also enables KPFM (AM-mode) investigations. For this, conductive coated (Cr/Pt, 5 nm/25 nm) micromachined monolithic silicon tips (Tap300E-G, r=25nm) from < 13 > "budget sensors" was supplied. In the AM-KPFM, the mapping of the topography and surface potential of the sample was performed in two-pass mode, in which first in tracing-pass the AFM in tapping mode collects the topographical data over the measuring profile line and this data is then used in retracing-pass at a set ascended height above the surface (<5 nm) to map the surface potential.
Scanning tunneling microscopy. The atomic structures were investigated using an Omicron low-temperature STM system at 77 K with a tungsten tip. Before characterization, the sample was degassed in situ at 500 °C for two hours.
Low-energy electron microscopy/ X-ray photoemission electron microscopy. There two sets of LEEM measurements were presented. The first (Figure 3 and Figure 6b) was   Structural model of the 6H-SiC(0001) substrate and schematics of the corresponding step patterns in the step retraction model. (a) Layer sequence of the Si-C bilayers in the 6H unit cell denoted as ABCACB. Each atomic layer is denoted by its atomic stacking sequence as hexagonal (h) or cubic (k) configuration. (b) Schematic side-view of 6H−SiC (0001) projected in (1120) plane with the six possible surface terraces S1*, S2*, S3*, S1, S2, S3. The surfaces Sn and Sn* (n = 1-3) are equivalent but rotated by 60° related to each other. The terrace widths are strongly reduced. A terrace width of ~240 nm is estimated for a miscut angle of 0.06° consistent with experimental results. The arrows mark the different retraction velocities of the Si-C layers in the step retraction model, which are related to the individual surface layer hexagonality. (c) Basic terrace step patterns of the 6H-SiC surface developing in the step retraction model. In the initial state, the individual S1, S2, and S3 terraces are separated by single SiC monolayer steps (1L) of ~0.25 nm in height. In the intermediate state, the S1 surface with the fastest retraction velocity has disappeared, and an alternating sequence of S2 and S3 surfaces remain with steps of ~0.25 nm (1L) above S2 and ~0.5 nm (2L) above S3. After advanced step retraction S2 becomes wider than the S3 terrace since the step velocity of S3 is faster than S2, which is depicted here. In the final state, the most stable S2 terraces remain with ~0.75 nm (3ML) in height.  (d) Two µ-LEED (E = 37 eV) patterns from neighboring areas with different dark-field LEEM contrast (marked by the green and violet dot in (b)) The 60° rotation of the satellite spots indicates the corresponding SiC crystal rotation. (e) Schematic step restructuring model of the 6H-SiC substrate during epi-graphene growth for three typical step patterns observed in the LEEM images (a) and (b). Buffer and graphene layers are not shown for clarity. Area (i) demonstrates the characteristic regular pattern of 1L/2L step pairs with the S3/S2 and S3*/S2* terrace sequence along line (i) in both LEEM images. The cyan-colored line-tracks indicate the different SiC crystal rotation below the terrace pairs S3/S2 and S3*/S2*, which give rise to the DF-LEEM contrast. Areas (ii) and (iii) with an irregular step sequence including ~0.75 nm (3L) steps fully explain the observed BF-and DF-LEEM contrast patterns along the line (ii) and (iii) in (a) and (b). (a) Scanning tunneling microscopy image of PASG monolayer graphene on 6H-SiC with nonidentical surface terminations measured in the area along the line type (iii) in the LEEM image of Figure 3a. The assignment of the surfaces (S2*, S2, S3*, and S2*) and the corresponding step heights are a direct result of the interpretation of the LEED images within the step retraction model and are schematically displayed in the area (iii) of Figure 3e. The images were recorded at 77 K with an Omicron low-temperature STM using a tungsten tip in the constant-current STM mode at 0.4 nA and 1.7 V. Atomic resolution STM images of the graphene buffer layer on neighboring terraces around the 3L, 2L, and 1L step edges, respectively, shown in (a). (b) shows the transition area from terrace S2* to S2, which is correlated with a 60° rotation of the SiC substrate, see the area (iii) in Figure 3a and e. This rotation manifests itself in a 60° rotation of triangular-shaped structures partly marked by the red/yellow triangles. For clarity, the directions of the triangles are sketched above each image. These triangular structures span a (6 × 6) nanomesh, which also rotates by 60° indicated by the blue diamond in the high-resolution insets. The buffer layer characteristic (6√3 × 6√3)R30° super-lattice is indicated by a yellow diamond and it follows the 60° rotation of the SiC surface. (c) The transition from an S2 to an S3* terrace is also characterized by a 60° rotation of the triangular structures, the (6 × 6) nanomesh, and the buffer layer superlattice. (d) For the S3* and S2* transition, no rotation of the triangles and, therefore, of the buffer layer is observed in agreement with the missing SiC crystal rotation.

Figure 5.
Quantitative measurements of surface potential and work function by Kelvin-Probe Force-Microscopy (KPFM) in amplitude mode (AM) of binary 1L/2L stepped monolayer graphene on Si-terminated 6H-SiC. (a) The AFM topography image allows an unambiguous assignment of the surface terraces S2 and S3 based on the step height sequence, as explained in the text. (b) Surface potential map from KPFM-AM measurement of the same surface area. The red areas mark bilayer graphene (BLG) spots, which have formed at a SiC defect. Marked are the positions of two line scans (green and magenta-colored lines) correlated with an S3 and an S2 terrace, respectively, for the histogram evaluation. (c) Histogram of the surface potential differences along the two line scans S2 (magenta) and S3 (green) indicated in the inset of (b). A clear difference of the potential values for the S2 and S3 surface is observed with VS2 − VS3 = 12 ±2 mV. A separation of ~60 mV to the potential values of the BLG is clearly visible. (d) Section of KPFM image in (b) (blue square) showing the potential contrast of monolayer graphene on the terraces S2 and S3. The green and magenta-colored rectangles (100 × 600 nm 2 ) indicate the area for the extraction of the potential values shown in (e). (e) Histogram of the surface potential difference (median values) extracted from the green (S3 terrace) and magenta (S2 terrace) rectangles shown in (d). A potential difference VS2 − VS3 = 9 ±2 mV is estimated.  (a) Two low-energy electron spectra (LEEM-IV) spectra taken at two different terraces S2 and S3, as indicated in (c). The inset shows the minimum position and a difference in energy of ~60 meV between the S2 and S3 curve. (b) The LEEM-IV map shows the lateral distribution of the minimum energy from the LEEM-IV spectra in an area of 4 µm × 3 µm. This LEEM-IV map is taken from the same area as the