Transfer doping of epitaxial graphene on SiC(0001) using Cs

Control of the charge carrier concentration is essential for applications of graphene. Here, we demonstrate the doping of epitaxial graphene on SiC(0001) via charge transfer from an adsorbed layer of Cs atoms with sub-monolayer coverage. The electronic structure of the graphene is analyzed using x-ray and angle-resolved photoelectron spectroscopy. In H-intercalated, quasi-freestanding monolayer graphene (QFMLG), the Dirac point can be tuned continuously from p-type to strong n-type doping. For strong n-type doping, analysis of the core level binding energies implies a deviation from a rigid band shift. This might be explained by an increased screening of the atomic core potential due to the higher number of charge carriers per C atom in the graphene layer. Furthermore, charge transfer into the SiC substrate leads to a change in band bending at the SiC/QFMLG interface, which saturates into a flat band scenario at higher Cs coverage. An analysis of the Fermi surfaces suggests an increasing electron-phonon-coupling in strongly doped QFMLG. In monolayer graphene (MLG), which is intrinsically n-type doped due to the presence of the buffer layer at the SiC interface, n-type doping can be enhanced by Cs evaporation in a similar fashion. In contrast to QFMLG, core level spectra and Dirac cone position in MLG apparently show a rigid band shift even for very high doping, emphasizing the importance of the substrate.


Introduction
Applications of graphene and other two-dimensional materials require control over the charge carrier concentration.This can be achieved in multiple ways, e.g. by using an electric gate voltage [1] or by substitution of C atoms in the graphene layer [2].An elegant way is the doping via surface charge transfer, which can be mediated either by chemical-a direct exchange of electrons between the graphene sheet and adsorbates-or electrochemical doping, in which the charge transfer is a result of redox reactions taking place near the graphene [2].Past studies have focused on a number of different doping species such as elements like potassium [3], bismuth, antimony, or gold [4], or molecules such as F4-TCNQ [5] and C 60 F 48 [6].In vertical van-der-Waals heterostructures, charge transfer doping of graphene has also been achieved by the deposition of atomically thin graphene oxide sheets [7], and by employing controlled defects such as boron or nitrogen vacancies in an adjacent hBN layer [8].By controlled doping of exfoliated graphene on SiO 2 using K deposition, Yan and Fuhrer [9] were able to understand how the presence of adsorbed dopant ions affects the transport properties of the graphene sheet.Surface charge transfer may even be used in applications such as molecular sensors [10,11].Epitaxial graphene in particular can also be doped via the intercalation of different elemental species to the interface [12,13].Since intercalation underneath epitaxial graphene provides a pathway towards novel 2D materials in its own right [14], the subsequent doping via alkali metal adsorption provides further insights into these heterostacks, as was demonstrated recently for graphene/2D-Ag/SiC [15].Very strong doping up until the van Hove singularity is expected to facilitate exotic ground states in graphene caused by strong correlation effects, and has been achieved via intercalation and chemical doping of epitaxial graphene on SiC [16][17][18].Charge transfer doping using cesium has been used in the past to facilitate n-type doping of epitaxial graphene [19].A lot of work has been done e.g. on graphene grown by chemical vapor deposition (CVD) on Ir(111): For example, Hell and Ehlen et al [20,21] were able to show a shift of the Dirac cone depending on Cs coverage, which turns into a flat band scenario if the graphene is sandwiched by both intercalated and adsorbed Cs layers.Cs doping is however not limited to elemental Cs, as ntype doping and a reduction of the work function have been achieved by wet-chemical doping using CsF and Cs 2 CO 3 on CDV graphene transferred to other substrates, and subsequently incorporated into optoelectronic devices [22].
Recently, Schröder et al [23] achieved strong ntype doping of graphene on Ir(111) via intercalation of Li, Eu, and Cs.It was shown that the respective shift of the core level binding energies and the position of the Dirac cone does not follow a rigid band model for higher doping.Presumably, this should also be the case for other doping mechanisms or graphene grown on different substrates, however it will remain unnoticed when only either core level or band structure measurements are used to assess doping.Here, we use the deposition of sub-monolayer thick Cs to achieve strong n-type doping in epitaxial graphene on 6H-SiC.Graphene on SiC is synthesized via the Ar-assisted sublimation growth [24,25], which offers high control over the thickness and uniformity of the as-grown graphene layers.Two different sample types were subjected to the experiments, one being epitaxial monolayer graphene (MLG), which rests on a carbon rich (6 √ 3 × 6 √ 3)R30 • reconstruction referred to as the buffer layer [26].The buffer layer is topologically identical to graphene, but electronically inactive due to covalent bonds with the Si atoms in the topmost SiC bilayer [26].On the other hand, a buffer layer can be converted into quasi-freestanding monolayer graphene (QFMLG) by breaking the bonds between the SiC substrate and the buffer layer via intercalation of foreign species.Here, we use hydrogen to passivate the dangling bonds, which in turn restores the well-known band structure of graphene [27,28].In the study presented herein, both sample types (MLG and QFMLG) are subjected to a stepwise deposition of Cs atoms, leading to a systematic increase in n-type charge carriers, as evidenced by x-ray and angle resolved photoelectron spectroscopy (XPS, ARPES).A special focus is placed on understanding the evolution of the Dirac cone and core level line shifts for very high doping in context of previous works.

XPS measurements on Cs doped QFMLG and MLG
First, we want to present the results of the XPS and ARPES measurements obtained by the evaporation of Cs on QFMLG.After being introduced into the UHV chamber, any adsorbates on the as prepared samples were removed via annealing.Afterwards, a step-wise evaporation of Cs was performed and XPS and ARPES measurements were carried out after each deposition step.A graphical summary of the analysis of the XPS and ARPES measurements can be found in figure 9 at the beginning of the Discussion section.The coverage of Cs on the surface after deposition was determined from the peak area of the Cs 3d 5/2 core level, which shows a steady increase with longer deposition times.To convert the Cs intensity in the XP spectrum into a number of Cs monolayers (ML), the system was calibrated prior by deposition of Cs on Cu(111), where it forms a ( √ 3 × √ 3)R30 • superstructure upon full monolayer coverage, corresponding to 5.87 × 10 14 Cs atoms per cm 2 (for more details, see the supplemental information).We estimate the uncertainty for the layer thickness termination to be about ±0.010 ML.
Due to the volatility and reactivity of Cs even in UHV [29], two individual QFMLG samples were prepared, one with low Cs coverages (denoted sample A) and one with higher Cs coverages (sample B).Core level spectra of the pristine sample A are shown in the bottom row of figure 1.The C 1s spectrum can be described by a symmetric component centered around 282.53 eV, which corresponds to C atoms bound in the SiC bulk, and an asymmetric component at 284.17 eV corresponding to the quasifreestanding graphene layer.The graphene component (G) is at lower binding energies than neutral graphene sheets as found e.g. in HOPG (284.45 eV) [30], indicating p-type doping.Additionally, a small secondary bulk component can be identified at 283.5 eV, accompanied by two almost vanishing components labeled S1 and S2 at 284.6 eV and 285.3 eV, respectively.These correspond to areas on the sample which are not intercalated and thus still covered by the buffer layer which is partially bound to the substrate [26], and will be elaborated on in more detail later.This is further evidenced by the corresponding Si 2p spectrum, which also shows two components at 100.25 eV and 101.24 eV.It should be noted that the energy difference between the components SiC H and SiC 6 √ 3 in the C 1s core level spectrum is not a chemical shift, but rather due to a difference in surface band bending as a result of a different bonding configuration at the interface in the corresponding areas [31].A graphical illustration showing the different types of possible bonding arrangements for C atoms at the SiC/graphene interface can be found in figure S.2 in the supplemental information.From the intensity of the SiC bulk components corresponding to H-intercalated and not-intercalated areas, it can be deduced that 91% of the sample is intercalated by hydrogen.
Upon deposition of small amounts of Cs, distinct changes in the spectra can be observed.Both the SiC H and G components are shifting to higher binding energies, which would suggest an increased ntype doping of the graphene layer as well as a change of the surface band bending of the SiC substrate [31,32].The transition from p-to n-type doping likely occurs at an intermediate Cs coverage between < 0.005 ML (E B (G) = 284.22eV) and 0.009 ML (E B (G) = 284.63eV).Furthermore, the shape of the spectrum in the graphene region changes, which leads to a broadening of the G component and requires a broad second component (labeled G Cs ) to adequately fit the data.Similar changes to the peak shape of the C 1s core level upon doping were observed e.g. for Rb, Cs, or K doped graphene sheets [19,33], as well as Gd-and Li-intercalated graphene on SiC [17,34], and Li-intercalated graphene on Ir(111) [23].However, Rosenzweig et al [35] also achieve strong doping of QFMLG via ytterbium intercalation and do not report such an additional component.In our analysis, we constrained the G component to keep a similar intensity ratio compared to the SiC bulk as for the pristine sample.Remarkably, the intensity of the component corresponding to the not intercalated buffer layer decreases and has completely vanished after deposition of 0.013 ML Cs.This indicates a complete decoupling of the buffer layer, which might have been facilitated by a partial intercalation of Cs.However, while Petrović et al [36] were able to succesfully intercalate Cs under graphene on Ir(111), experiments carried out with Cs deposited on graphene on SiC did not show signs of intercalation [19,37].The origin of the component G Cs is not yet fully understood [19,23], and has been attributed to an increased formation of electron-hole pairs in the past [33].In a theoretical treatment by Sernelius [38], the asymmetry of the graphene peak is found to increase significantly for high doping levels exceeding 10 12 cm −2 due to emerging channels for the excitation of electronhole pairs as well as 2D plasmons.Similarly, by calculating the full spectral function of doped graphene, Despoja and Šunjić [39] show an increasing asymmetry of the G peak and the appearance of discrete 2D plasmon peaks for high doping concentrations.
Selected C 1s core level spectra of the QFMLG sample B with higher Cs coverages are shown in figure 2. The maximum coverage that was achieved were 0.657 ML Cs after a total deposition time of 180 min.In comparison to the pristine QFMLG sample (indicated by dashed lines in figure 2), the SiC H and G components are initially shifting to higher binding energies.At higher coverages, the SiC H bulk component does not change further, indicating a flatband scenario.The corresponding Si 2p core level (not shown) shows the same behavior.The G component reaches a maximum binding energy of 285.07 eV at a Cs coverage of 0.125 ML and subsequently starts to shift back to lower binding energies.Similar to the observations made on sample A, the shape of the C 1s peak is further distorted with higher doping, indicated by the increased intensity and broadening of the G Cs component.In contrast to G, the binding energy of G Cs continues to increase with higher coverage.
The electronic structure of MLG differs from quasi-freestanding graphene due to the presence of the buffer layer at the SiC/graphene interface.Here, interface states lead to an n-type doping of the graphene layer [40,41].C 1s core level spectra for pristine MLG samples are shown in the bottom row of figure 3. Similar to the case of QFMLG described above, the spectrum consists of a symmetric component centered around 282.8 eV corresponding to C atoms bound in the SiC bulk (labeled SiC 6 √ 3 ), and an asymmetric component corresponding to the graphene layer (G).The binding energy of the G peak at 284.6 eV is indicative of the aforementioned n-type doping.Two additional components are required to fit the data, which correspond to C atoms in the buffer layer.Atoms still covalently bound to the SiC substrate are denoted as S1 (284.9 eV), while those bound only within the buffer layer are labeled as S2 (285.7 eV) [26].The corresponding Si 2p core level spectra (not shown) also feature two components, with the one corresponding to Si atoms bound in the bulk appearing at 101.5 eV.The second component shows a chemical shift of 0.42 eV to higher binding energies and can be explained by Si atoms at the interface binding to the buffer layer [26].Deposition experiments were carried out in a similar fashion as for the QFMLG samples presented above, with one sample being prepared with lower (MLG A) and one with higher (MLG B) Cs coverage.It should be remarked that apparently Cs has a much higher sticking coefficient on MLG compared to QFMLG, as the coverage determined from XPS is about a factor of 5 to 10 higher after similar deposition times.The maximum coverage that was achieved were 0.79 ML Cs after a total deposition time of 18 min.After the deposition of Cs, distinct changes to the C 1s spectrum can be observed (figure 3).Since the presence of the buffer layer components complicates the peak analysis, a few assumptions had to be made during fitting: Since the buffer layer is not electronically active, it is reasonable to assume that S1 and S2 will not change in energy relative to the SiC 6 √ 3 bulk component.With increased Cs coverage, the intensity of SiC 6 √ 3 , S1, and S2 will be attenuated by the same amount, so that S1 and S2 may readily be constrained to the SiC bulk component.The remaining signal is then due to the graphene layer.However, how this should be modeled is not intuitively clear, and different approaches may lead to similarly good results.We decided to pursue two different avenues, starting from the premise that the intensity of the G peak relative to SiC 6 √ 3 should remain constant, as in a first approximation it is only related For small coverages, the binding energy is found to increase by up to 0.7 eV, whereas it decreases again for higher coverage.It appears as though the binding energy of Cs 3d5/2 might saturate for high coverage.
to the number of carbon atoms in the graphene layer.As such, we treated the G peak as a broadened asymmetric line shape similar to the previous analysis of QFMLG assuming a constant G : SiC 6 √ 3 ratio.As can be seen from figure 3, this leads to a reasonable agreement between the fit and the experimental data.With increasing Cs coverage, the G component broadens and shifts to higher binding energies, reaching a maximum of 285.75 eV for 0.68 ML Cs.This implies an increased n-type doping similar to the QFMLG.The binding energy of SiC 6 √ 3 remains almost constant, indicating that there is no change in band bending.However, the second component G Cs -which is very prominent on QFMLG samples even for smaller coverages-is notably absent for this approach.If G Cs is indeed related to the excitation of 2D plasmons as discussed previously [38,39], its absence may be related to slight differences in the plasmon dispersion in MLG and QFMLG [42].
Another attempt was made to include G Cs in the analysis, which is shown in figure S.3 in the supplemental information.However, this requires to relinquish the assumption of a constant intensity ratio of G : SiC 6 √ 3 .Instead, a fit which keeps ratio of the sum of G + G Cs to SiC 6 √ 3 constant leads to a similarly good agreement as the procedure shown in figure 3.More insight could probably be gained by a variation of the energy of the incident x-ray photon, which can enhance surface sensitivity and ease to distinguish between spectral contributions from graphene and the buffer layer.
Finally, we want to briefly discuss the Cs 3d spectra corresponding to the adsorbed Cs atoms.As described above, the intensity of the Cs 3d 3/2 core level is a measure of the thickness of the adsorbed Cs layer.The high resolution core level spectra can be modeled using a symmetric line shape for low Cs coverages (below ≈0.05 ML), while the peak shape shows a slight asymmetry for higher coverages.In general, such an asymmetry is indicative of metallic behavior [43].Figure 4 shows the binding energy of Cs 3d 3/2 for all measurements.The binding energy initially shows a significant increase for small coverages, shifting by approximately 0.7 eV.For coverages above ≈0.05ML Cs, the binding energy decreases again, apparently saturating around a value of 726.5 eV.The increase in binding energy could be linked to an reduced screening of the core potential after donation of the lone valence electron into the graphene layer, while the subsequent decrease might be caused by mutual interactions between the Cs atoms upon forming larger clusters.In a scanning tunneling microscopy study, Song et al [37] discovered that Cs atoms tend to form ordered superlattices at lower temperatures, preferably on bi-and multilayer graphene on SiC.However, low-energy electron diffraction (LEED) diffraction experiments showed no signs of such structures forming on the samples discussed here.This is not surprising, as our samples have predominantly monolayer coverage due to the argon assisted sublimation growth, and deposition of Cs was carried out at room temperature.

ARPES measurements
ARPES measurements were carried out after each deposition step on both sample types.Figure 5 shows measurements on QFMLG around the K point for increasing Cs coverage.Pristine QFMLG (figure 5(a)) is p-type doped, which can clearly be seen from the measurement of the Dirac cone (top row): The linear bands intersect above the Fermi level, leading to a position of the Dirac point (E D − E F ) = −0.30eV, in agreement with previous work [44].With the deposition of Cs, electrons are donated into the graphene sheet, leading to a shift of E D below E F .Consistent with the XPS measurements described above, the transition from p-to n-type doping occurs at a Cs coverage between 0.002 ML and 0.009 ML.The graphene layer becomes increasingly n-type doped with increased Cs coverage.Another important observation that can be made, is that the linear bands show a kink directly at the K point.As a consequence, the cone appears elongated along the energy axis and shows a slight offset between the upper and lower parts of the cone above and below E D .Similar observations have been made previously on MLG samples by Bostwick et al [45], and have been attributed to many-body interactions such as electron-electron, electron-plasmon and electronphonon coupling.The extend of these features was found to scale with doping on potassium doped MLG [45].Unfortunately, the limited resolution of the labbased ARPES system used on the Cs doped samples presented here does not suffice to verify these predictions.The bottom row in figure 5 shows constant energy cuts at the Fermi energy.The intensity of the Fermi surface varies along the k x direction, a phenomenon known as the dark corridor effect [46].The overlay in figure 5 shows the Fermi surface contour according to third-nearest neighbor tight binding calculations, which were performed based on the works by Reich et al and Kundu [47,48].As expected, the experimental Fermi surface appears circular close to the Dirac point, as can be seen e.g. for pristine or slightly n-type doped QFMLG (figures 5(a)and (b)).For intermediate doping (figure 5(c)), the Fermi surface starts to deform away from the circular shape, but still shows an excellent agreement between experiment and theory.For very high doping levels with (E D − E F ) ≳ +1.30 eV, as shown exemplarily for a coverage of 0.657 ML Cs in figure 5(d), the experimentally observed Fermi surface contour deviates strongly from the calculated tight-binding band structure, showing a distinct triangular shape.This trigonal warping has been observed e.g. for highly doped graphene just below the van Hove singularity by McChestney et al [16].
The ARPES measurements performed on the MLG samples in principle showed a similar behavior as those on QFMLG.As can be seen in figure 6(a), pristine MLG is already n-type doped due to charge transfer from interface states of the buffer layer [40,41].As such, the Dirac point is located 0.43 eV below E F , consistent with literature reports [49,50].Upon the deposition of Cs, the Dirac point continuously shifts further down, indicative of increased n-type doping in good agreement with the XPS data.The Fermi surface contour again initially closely follows the prediction by our tight binding calculations, but also shows strong trigonal warping for (E D − E F ) ≳ +1.30 eV, consistent with the observations made on the QFMLG samples.An example is shown in figure 6(b) for a Cs coverage of 0.79 ML.
The position of the Dirac point can also be used to determine the carrier concentration in the graphene sheet.The number of charge carriers per C atom in the graphene layer is where A F is the area of the Fermi surface contour of a single Dirac cone, and A U is the size the inplane unit cell of graphene [23].We determined A F for different values of E D from the aforementioned tight binding calculations.From equation (1), one can easily deduct the carrier concentration per cm 2 , which is shown for QFMLG and MLG in figure 7 depending on the Cs coverage.Pristine QFMLG is p-type doped with a hole concentration of 8.9 × 10 12 cm −2 , while pristine MLG is n-type doped with 1.8 × 10 13 electrons per cm 2 , both in good agreement with literature [49].As can be seen from figure 7, the carrier concentration increases almost linearly with increasing Cs coverage, before potentially saturating around 1.9 × 10 14 −2.3 × 10 14 cm −2 for high Cs coverage.Since the shape of the Fermi surface deviates from the tight binding calculations for high doping (see e.g.figures 5(d) and 6(b)), an upper limit for the the carrier concentration was determined for these coverages by manually approximating A F in the constant energy cuts in the ARPES measurements.These are shown as error bars in figure 7 and amount  to a maximum of approximately 3.3 × 10 14 cm −2 for QFMLG and 2.4 × 10 14 cm −2 for MLG.

Determination of the work function
Finally, we want to investigate how the continued deposition of Cs on the surface of the graphene sheet effects its work function Φ G .In photoemission, Φ can be determined via the secondary electron cut-off (SEC) [51].Here, the work function is equal to the difference of the incident photon energy hν and the width of the measured spectrum from the Fermi edge E F to the SEC: In order to ensure that the vacuum energy E vac of the sample is above that of the analyzer and that electrons from the SEC (which would have zero kinetic energy) can reach the spectrometer, a negative bias voltage of U B = −7V is applied to the sample.The result of this measurement is shown in figure 8 by plotting Φ G over the position of the Dirac cone (E D − E F ).For the pristine samples, the work functions are 4.7 eV and 4.0 eV for QFMLG and MLG, respectively, in excellent agreement with previous work [49].According to Mammadov et al [49], in a rigid band picture, the work function of graphene should scale linearly with the position of the Dirac point, where Φ HOPG = 4.55(0.05)eV is the work function of HOPG [49], which may be used as a reference for neutral graphene.As can be seen in figure 8, Φ G of Cs doped graphene does not follow this rigid linear shift, but decreases much faster upon the deposition of Cs.For higher doping (E D − E F > 0.51 eV), Φ G changes with the same slope as in the rigid band picture, but with a constant energy offset of approximately 0.9 eV.This offset can be explained by the presence of an interface dipole moment due to the positively charged Cs ions and negatively charged graphene layer, which lowers E vac (and therefore Φ G ) [52].

Discussion
The most important results from the XPS and ARPES measurements are summarized in figure 9.With increasing coverage of the deposited Cs layer, systematic changes of the core level binding energies of graphene (with the two components G and G Cs ), the position of the Dirac point (E D − E F ), and the band bending are observed.The band bending can be deducted from the position of the SiC bulk component in the C 1s core level spectrum, as described previously [53].
For QFMLG, the binding energy of G initially closely follows the change of the position of the Dirac point, as can be expected from a rigid band model: electrons that are added to the π band of graphene lead to a lowering of E D , and the C 1s core level shifts by the same amount.This is best understood by using a band diagram as shown in figure 10.The p-type doping of pristine QFMLG on 6 H-SiC (figure 10(a)) results from the interplay of two distinct doping mechanisms: (i) Breaking of the crystal symmetry along the [0001] direction leads to a spontaneous polarization (SP) inherent to hexagonal SiC polytypes [41,44,54].This SP results in negative (pseudo-)charges at the surface of SiC(0001), which were shown to introduce holes in the adjacent QFMLG layer, thus producing the p-type doping observed [41,44].(ii) The surface band bending V bi observed for the SiC bulk leads-for n-type SiCto a depletion layer of positive areal charge density, partially balancing the negative (pseudo-)charges and effectively reducing the number of holes in QFMLG [44].The surface charge density q sc can be estimated from the observed band bending and amounts to 2.75 × 10 12 cm −2 for the pristine QFMLG sample, in good agreement with previous measurements on similar n-type 6H-SiC [44].We note in passing that the inelastic mean free path of photoelectrons in XPS is short compared to the width of the space charge region [53], so that only the energetic position of the bands and core levels directly at the interface is probed.
Upon the deposition of Cs, electrons are donated into the graphene layer, as evidenced by both a shift of the G component in XPS as well as (E D − E F ) to higher binding energies.The band bending is reduced as well, which can be explained if negative charge carriers, e.g.electrons, occupy the positive hole states in the depletion zone at the interface.This effectively lowers the upwards band bending, as can be seen in figure 10(b).For larger Cs coverages, the position of the Dirac point continues to shift to higher binding energies, showing increased n-type doping of the graphene layer.The band bending drops to zero at coverages above 0.42 ML Cs and remains unchanged if additional Cs is added.This is due to a complete neutralization of the space charge region, which leads to a flat band scenario as shown in figure 10(c).
In a simple rigid band picture, one would assume that the G component in the C 1s core level spectrum continues to shift with the Dirac point.As can be seen from figure 9(a), this is not the case here.After reaching a maximum, the G component shifts back to lower binding energies.A similar behavior was observed by Schröder et al [23] for Li intercalated graphene on Ir(111).Interestingly, the second component G Cs continues to follow the shift of the Dirac point to higher E B even for very high coverages.
On MLG samples (figure 10(d)), the situation is different due to the presence of the buffer layer.Here, pristine samples show an n-type doping of the graphene layer due to charge transfer from  interface states, overcompensating for the aforementioned doping mechanisms [26,40,41].These interface states also affect the space charge region in the SiC, resulting in only a small upwards band bending of 0.06 eV, in good agreement with previous measurements [32].With increasing amount of deposited Cs, the Dirac point as well as the component G of the C 1 s core level shift to higher binding energies, consistent with a higher concentration of electrons.The energy shift for both is similar, indicating that for MLG-in contrast to QFMLG-a rigid band model for the graphene sheet may be valid.However, due to the complicated fitting procedures of the C 1s core level spectra of MLG (figure 3), the uncertainties on the peak positions are rather large compared to QFMLG.As expected, the band bending remains mostly unaffected, as the substrate Fermi level is pinned by the interface states.Note that for MLG, the second component G Cs may or may not be present, depending on how the data is analyzed (see The validity of a rigid band approximation can be easily visualized by plotting the C 1s core level binding energy (BE) of the graphene component G versus the position of the Dirac point (E D − E F ) as obtained from ARPES.This is shown in figure 11(a), with HOPG as an additional reference point for neutral graphene at 284.45 eV [30].The dark dashed line corresponds to the expected trend as predicted by a rigid band shift with For small doping, the data points for the QFMLG samples nicely follow this rigid band shift.However, for larger doping, there is a large deviation from the rigid band model, as the binding energy of the G peak in XPS is decreasing rather than increasing.This counterintuitive shift of G at high doping levels has been observed before [23].Schröder et al [23] attribute this to a so far unexplained effect counteracting the rigid band shift, which scales with the transferred charge per C atom in the graphene layer (∆Q from equation ( 1)).This is evident from the gray solid line in figure 11(a), which describes the deviation from the rigid band model to be proportional to ∆Q.The proportionality constant can be obtained by plotting ∆E vs. ∆Q (as shown in figure 11(b)), and making a linear fit to the data.As can be seen, the data points for QFMLG do represent a linear trend fairly well, with a slope of (−21.9 ± 1.0) eV, which is of the same order of magnitude as the value of (−18.2 ± 0.9) eV reported by Schröder et al [23].The variation is likely due to the difference in sample preparation, as we use quasifreestanding graphene on SiC doped via adsorbed Cs, while they use Li intercalated graphene on Ir(111).The red curve in figure 11(a) thus accurately describes the core level shift for higher doping.
A second observation that can be made from figure 11(a) is that the core level shift in MLG shows a distinctly different behavior than in QFMLG.The data points appear to rather show a linear trend, consistent with a rigid band model.However, an extrapolation of the data points (light gray dashed line in figure 11(a)) suggests a different binding energy of G at the charge neutrality point for MLG samples of around 284.23 eV, which is also sometimes given as the BE for graphite [23].It seems reasonable to assume that the different behavior of MLG and QFMLG is caused by the presence of the buffer layer.Previous studies [55,56] suggest that in contrast to the very flat structure of the graphene sheet in QFMLG, MLG has a comparatively large surface roughness and inhomogenous charge distribution due to the buffer layer at the interface, which might have an effect on the doping behavior.As such, it would be of interest to achieve strong p-type doping of MLG samples to study this effect over a wider range of Dirac point positions.Such experiments have already been carried out in the past by using electronwithdrawing molecules like F4-TCNQ [5] or C 60 F 48 [6].Unfortunately, in these works no analysis of the C 1s core level shift is given, which is understandable since the presence of organic molecules will add further components in the C 1s region.Elemental acceptors such as as Bi, Sb, or Au have also been used to achieve p-type doping, but no core level spectroscopy is provided in this study either [4].

Conclusions
To summarize, we were able to achieve strong n-type doping in epitaxial MLG and H-intercalated QFMLG on 6H-SiC(0001) by a step-wise deposition of Cs atoms.Our systematic XPS and ARPES study is consistent with the previously proposed model of polarization doping in epitaxial graphene on polar substrates [41].The position of the Dirac point can be tuned continuously, and the shape of the Fermi surface is consistent with tight-binding calculations for low and intermediate coverages [47,48].If doped close to the van Hove singularity, the Dirac cone is distorted and shows strong trigonal warping.The sample work function was obtained from photoemission experiments and is found to follow a linear trend similar to a rigid band shift, but is offset energetically by an interface dipole moment on the order of 0.9 eV.Analyzing ARPES and XPS core level shifts in unison shows a clear deviation from a rigid band model for highly doped QFMLG.This can be described in good agreement with a model proposed by Schröder et al, in which the difference between the observed core level shift and the rigid band model scales linearly with the accepted charge in the graphene layer.In contrast, our data suggests the validity of a rigid band model for MLG even for high doping, likely due to the presence of the buffer layer at the interface.

Experimental details
Epitaxial graphene samples (MLG) were prepared using the Ar-assisted sublimation growth on SiC described in detail elsewhere [24,25].SiC wafers were purchased from NOVASiC.To produce QFMLG, first a buffer layer sample is grown, which is then annealed in an H-atmosphere of 800 mbar at 550 • C for 15 min to intercalate H to the interface and decouple the buffer layer [27,28].
The evaporation of Cs is achieved in-situ from a custom built evaporator, which is equipped with commercially available dispensers from SAES Getters.In the dispenser, Cs is bound in Cs 2 CrO 4 , and is released into the gas phase by a reduction reaction with the getter material ST 101 (Zr 0.84 Al 0.16 alloy) upon annealing via a direct current on the order of 4.7−5.7A.Prior to experiments, the dispenser is degassed for 10 min above 700 • C.During evaporation on the graphene samples, the dispenser was operated at approx.600 • C.
XPS and ARPES were performed in a dedicated system by SPECS, equipped with a monochromatic SPECS Focus 500 Al-Kα X-ray source, monochromatic SPECS UVS 300 UV source for linear polarized He-I and He-II radiation, and a SPECS Phoibos 150 hemispherical analyzer with 2D-CCD detector.The accuracy of the binding energies of fitted components in XPS spectra is usually around ±0.10 eV or better, but may be worse in case of overlapping components.The accuracy for the determination of the Dirac point from ARPES measurements is on the order of 20 meV (the coverage factor of all reported uncertainties in the manuscript corresponds to k = 1 (e.g. one σ)).For LEED, a SPECS ErLEED 150 was available.The base pressure of the UHV system during evaporation and analysis was better than 3 × 10 −10 mbar.

Figure 1 . 6 √ 3 )
Figure 1.XPS (a) C 1s and (b) Si 2p core level spectra of pristine (bottom row) and Cs covered QFMLG up to a coverage of 0.013ML.Only 91% of the pristine sample is intercalated by H, leading to the presence of non-intercalated SiC bulk component (SiC 6 √ 3 ) and buffer layer components S1 and S2.Vertical dashed lines indicate the positions of the SiCH and G components of the pristine sample.

Figure 2 .
Figure 2. Selected XPS C 1s core level spectra of QFMLG sample B with high Cs coverages.Dashed vertical lines indicate the binding energies of the SiCH and G components of pristine QFMLG.

Figure 3 .
Figure 3. XPS C 1s core level spectra of pristine (bottom row) and Cs covered MLG.(a) Sample A was used for short deposition times up to a coverage of 0.15 ML Cs, while (b) sample B was deposited with thicker layers up to 0.79 ML Cs.Vertical dashed lines indicate the positions of the SiC 6 √ 3 and G components for the pristine samples, respectively.

Figure 4 .
Figure 4. Cs 3d5/2 binding energies determined from XPS core level spectra for QFMLG and MLG samples for varying Cs coverages.Dashed lines are added as a guide to the eye.For small coverages, the binding energy is found to increase by up to 0.7 eV, whereas it decreases again for higher coverage.It appears as though the binding energy of Cs 3d5/2 might saturate for high coverage.

Figure 5 .
Figure 5. Energy-momentum cuts slicing through the Dirac cone of graphene measured along the Γ − K direction (top row) for selected Cs coverages on QFMLG.The bottom row shows the corresponding Fermi surface, with an overlay of the Fermi surface contour according to tight-binding calculations.For high Cs coverage, shape and size of the Fermi surface strongly deviate from the calculation.

Figure 6 .
Figure 6.Energy-momentum cuts slicing through the Dirac cone of graphene measured along the Γ − K direction (top row) for pristine MLG and after deposition of 0.79 ML Cs.The bottom row shows the corresponding Fermi surface, with an overlay of the Fermi surface contour according to tight-binding calculations.As for QFMLG, shape and size of the Fermi surface strongly deviate from the calculation for high Cs coverage.

Figure 7 .
Figure 7. Carrier concentration in Cs doped graphene on SiC derived from the position of the Dirac point in ARPES.Dashed lines are added as a guide to the eye.Error bars for high Cs coverages provide an upper limit for the carrier concentration based on the area of the Fermi surface.

Figure 8 .
Figure 8. Experimentally determined work function ΦG of QFMLG and MLG samples relative to the position of the Dirac point (ED − EF).The gray dashed line shows the expected behavior according to a rigid band model starting from HOPG as a reference point[49].The red dashed line has the same slope, but is offset by 0.9 eV.

Figure 9 .
Figure 9. Plot of the binding energies of the components G and GCs in the C 1s core level spectra (top row), band bending (bottom row, left axis), and position of the Dirac Point (ED − EF) (bottom row, right axis) versus the coverage with Cs for (a) QFMLG and (b) MLG samples.

Figure 10 .
Figure10.Band diagrams of (a) pristine QFMLG on n-type 6H-SiC, and QFMLG after deposition of (b) 0.05 ML and (c) 0.66 ML Cs.EC and EV denote the conduction band minimum and valence band maximum, respectively.The spontaneous polarization of the SiC leads to negative (pseudo-)charges at the interface (light gray symbols).Charge neutrality at the interface is achieved by an upwards band bending V bi accompanied by a depletion zone hosting a positive space charge, and holes (black symbols) being induced in the graphene layer.Upon the deposition of Cs, electrons are transferred into graphene, causing a shift of the Dirac point ED below EF in combination with an increasing binding energy of G, a shift of SiCH indicating reduced band bending, and a decreasing work function ΦG.For MLG samples (d), additional states at the interface are provided by the buffer layer (BL), fixing the surface Fermi level and overcompensating the doping caused by the spontaneous polarization.

Figure 11 .
Figure 11.(a) Binding energy of the component G in the C 1 s core level spectra plotted versus the position of the Dirac Point (ED − EF).The dark dashed line indicates the expected trend from a simple rigid band model with HOPG as a reference for neutral graphene [30].The grey solid line corresponds to the empirical curve by Schröder et al [23], while the red solid line employs the same model based on figure 11(b).(b) Deviation from the rigid band model ∆E versus charge carriers per C atom ∆Q.The dashed line is a linear fit to the QFMLG data.