# Surface Transport Properties of Pb-Intercalated Graphene

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{−1}onto the BL sample kept at 200 ${}^{\circ}$C. Thereafter the sample was heated for 5 min at 500 ${}^{\circ}$C. In a second cycle 10 MLs of Pb are deposited onto the sample at room temperature. Finally, the sample was heated again for 5 min at 500 ${}^{\circ}$C. The temperatures were measured by a pyrometer.

_{α}radiation (1486.6 eV) was used and the photoelectrons were analyzed with a Specs Phoibos 150-MCD analyzer. ARPES measurements were performed with HeII radiation (40.82 eV) using a Specs UVS 300 He-lamp in conjunction with a Specs TMM304 monochromator and a Specs Phoibos 150 analyzer with a 2D-CCD-detector. The sample investigated by XPS and ARPES had to be exposed to air. Annealing at 320 °C in UHV resulted in the desorption of contaminants, e.g., oxygen.

## 3. Results and Discussion

#### 3.1. Structural Properties

#### 3.2. Photoemission Spectroscopy

_{C}(101.8 eV) belongs to the Si atoms of the substrate which are bonded to the BL. Two further components can be seen, whereby the component SiC’ (100.4 eV) refers to Si atoms of the SiC substrate beneath intercalated areas of the sample. Finally, the component Si

_{Pb}(99.8 eV) can be attributed to the Si atoms which are bond to the intercalated Pb atoms. The energy shift between the SiC and SiC’ components of both, the Si2p and the C1s spectrum, is comparable. Furthermore, the intensity ratio of the SiC’ and SiC component is the same for the C1s and the Si2p spectrum.

_{7/2}-state which is in good agreement of the bulk value measured for pure Pb [48]. The concomitant metallic behavior is manifested by the strong asymmetry of the peaks due to many-electron interaction effects in metals [49]. From STM measurements we know that all remaining Pb on the sample lies beneath the graphene. Two approaches for estimating the thickness of the intercalated Pb layer have been chosen: (I) A three layer model (from top to bottom: graphene–Pb–SiC) yields to a thickness of ${d}_{\mathrm{Pb}}=3.3$ Å. This model compares the intensity ratio of the 7/2-peak of the Pb4f core level and SiC’ intensity of the C1s peak with the product of the ratio of the corresponding cross sections, the ratio of the atomic density of Pb and SiC and the weakening of the signal in the Pb layer. This weakening can be described by an exponential function of the ratio of the Pb layer thickness and the inelastic mean free path in Pb. (II) This approach only takes the different signals in the C1s core level into account. A comparison of the intensity ratio of the SiC’ peak and the graphene signal with the intensity ratio of the SiC signal (not intercalated) and the BL components multiplied with the weakening in the Pb layer yields to ${d}_{\mathrm{Pb}}=6.9$ Å. Again, an exponential function of the ratio of the Pb layer thickness and the inelastic mean free path in Pb describes the reduction in the Pb layer. Furthermore, we take a MLG coverage of 10 % prior to the intercalation into account. Thus, using XPS an average Pb thickness of 5.1 ± 1.8 Å is estimated, which is well above the (111) inter-plane distance of a fcc Pb crystal (2.85 Å), while the first approach was chosen to include two energetically clearly separated peaks, the second one minimizes systematic and energy-dependent errors. Nevertheless, XPS finds prominently multiple layers of intercalated Pb underneath the decoupled graphene supporting the expectations from distinct contrast changes in STM between different areas hosting the characteristic features of intercalation.

_{D}is less than 50 meV above the the Fermi level E

_{F}, yielding a low charge (p-type) carrier density of $p={({E}_{D}-{E}_{F})}^{2}/\left({\hslash}^{2}{v}_{F}^{2}\pi \right)=2\times {10}^{11}$ cm${}^{-2}$. The spectrum is superimposed by a second Dirac cone. The Dirac point is around 0.5 eV below E

_{F}, thus reminiscent of n-type doped monolayer graphene (MLG) [35]. The BL sample, which we used, was slightly overgrown (10%), i.e., MLG was present at the SiC step edges. Here, this MLG fraction serves as a reference. Moreover, it also seems that Pb intercalation in this area barely took place.

#### 3.3. In-Situ Surface Transport Measurements

_{2}, i.e., at lower temperatures the proximity coupling may become more severe.

## 4. Summary and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**Intercalation process studied by electron diffraction. Sequence of SPALEED images (taken at 100 eV electron energy) of (

**a**) pristine BL/SiC(0001), (

**b**) after adsorption of 5 MLs of Pb and (

**c**) after intercalation of Pb (after adsorption of 5 + 10 ML Pb and annealing cycles). (

**d**) Zoom of the (00)-spot after intercalation of Pb (marked in (

**c**)). (

**e**) Line scans taken along the $\left[1\overline{1}00\right]$-direction for the phases shown in panels (

**a**–

**c**). The new reconstruction spots upon Pb intercalation are marked by blue and yellow arrows.

**Figure 2.**(

**a**) Schematic showing the defect generation by Ar-sputtering on one half of the BL/SiC(0001) system. (

**b**) SPALEED images of the vicinity of the (00)-diffraction spot after the Pb intercalation procedure (5 ML adsorbed followed by annealing) performed simultaneously on the non-sputtered (top) and sputtered (bottom) part of the sample. ($E=100$ eV). (

**c**) Decomposition of the (00)-spot into a central peak (Gaussian) and shoulder (Lorentzian) ($E=114$ eV, $S\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}4.4$). (

**d**) G(S) analysis of the clean and sputtered surface (black, red) and Pb intercalation (blue). The measurements were performed at $T=300$ K.

**Figure 3.**(

**a**) Large scale SEM image of the intercalated area. The dark contrast refers to residual (insulating) BL areas. (

**b**–

**d**) STM images of various phases after intercalation of Pb revealing both striped and bubble-like modulations ((

**b**) −0.5 V, 1 nA; (

**c**) −0.2 V, 0.02 nA; (

**d**) −1 V, 0.2 nA). MLG and BL label non-intercalated monolayer graphene and buffer layer areas, respectively. (

**e**) STS spectra on two different striped phases (set point −0.5 V, 0.5 nA). The measurements were performed at LN

_{2}temperature. (

**f**) Height profiles across various striped phases.

**Figure 4.**XPS spectra of partially Pb-intercalated BL/SiC. (

**a**) C1s, (

**b**) Si2p and (

**c**) Pb4f state. (

**d**) ARPES spectrum around the K-point of graphene. The measurements were performed at $T\phantom{\rule{3.33333pt}{0ex}}=\phantom{\rule{3.33333pt}{0ex}}300$ K.

**Figure 5.**(

**a**) IV-curves on Pb-intercalated graphene ($T=300$ K). For reference, the IV-curves of QFMLG and MLG are shown as well ($s=30$ µm). (

**b**) Rotational square measurement for a fixed tip distance of 100 µm. The inset shows a SEM image of the tip assembly ($T=300$ K). (

**c**) Sheet resistance ${R}_{\mathrm{sh}}$ as a function of the tip spacing s. The inset shows the collinear probe geometry ($T=300$ K). (

**d**) Sheet resistance as a function of temperature for a fixed collinear probe configuration ($s=30$ µm). (

**e**) Anderson plot of the data shown in panel (

**d**) covering the temperature range down to 60 K. (

**f**) Arrhenius analysis of the transport data shown in panel (

**d**). The low temperature regime reveals an activation energy of 13 meV.

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**MDPI and ACS Style**

Gruschwitz, M.; Ghosal, C.; Shen, T.-H.; Wolff, S.; Seyller, T.; Tegenkamp, C.
Surface Transport Properties of Pb-Intercalated Graphene. *Materials* **2021**, *14*, 7706.
https://doi.org/10.3390/ma14247706

**AMA Style**

Gruschwitz M, Ghosal C, Shen T-H, Wolff S, Seyller T, Tegenkamp C.
Surface Transport Properties of Pb-Intercalated Graphene. *Materials*. 2021; 14(24):7706.
https://doi.org/10.3390/ma14247706

**Chicago/Turabian Style**

Gruschwitz, Markus, Chitran Ghosal, Ting-Hsuan Shen, Susanne Wolff, Thomas Seyller, and Christoph Tegenkamp.
2021. "Surface Transport Properties of Pb-Intercalated Graphene" *Materials* 14, no. 24: 7706.
https://doi.org/10.3390/ma14247706