Microscopic correlation between chemical and electronic states in epitaxial graphene on SiC$(000\overline{1})$

We present energy filtered electron emission spectromicroscopy with spatial and wave-vector resolution on few-layer epitaxial graphene on SiC$(000\overline{1})$ grown by furnace annealing. Low-energy electron microscopy shows that more than 80% of the sample is covered by 2–3 graphene layers. C1s spectromicroscopy provides an independent measurement of the graphene thickness distribution map. The work function, measured by photoelectron emission microscopy (PEEM), varies across the surface from 4.34 to 4.50 eV according to both the graphene thickness and the graphene-SiC interface chemical state. At least two SiC surface chemical states (i.e., two different SiC surface structures) are present at the graphene/SiC interface. Charge transfer occurs at each graphene/SiC interface. $k$-space PEEM gives 3D maps of the $\left|{\mathrm{k̄}}_{\parallel }\right|$ $\pi -{\pi }^{*}$ band dispersion in micron-scale regions showing that the Dirac point shifts as a function of graphene thickness. Bragg diffraction of the Dirac cones via the superlattice formed by the commensurately rotated graphene sheets is observed. The experiments underline the importance of lateral and spectroscopic resolution on the scale of future electronic devices in order to precisely characterize the transport properties and band alignments.

Figure 1

LEED patterns from a nominally 3-layer C-face graphene sample with primary electron energy of (a) 76 eV and (b) 126 eV.

Figure 2

(a)–(c) Typical LEEM images ($10\hspace{0.5em}\mu$m FoV) of the graphene surface as a function of electron energy (a) 3.0 eV and (b) 4.8 eV. (c) Reflectivity spectra extracted along the dotted line in (b) showing clearly the variation in the number of intensity minima and therefore the number of graphene layers.

Figure 3

(a) Typical reflectivity curves extracted from the LEEM data set showing 0 to 3 oscillations below 7.5 eV. (b) Graphene thickness map (FoV $=10\hspace{0.5em}\mu$m) generated by counting the number of minima in the reflectivity curves.

Figure 4

The position (boxes) of dips in reflectivity curves from Fig. 2c and Fig. 3a, compared with theoretical estimation based on tight-binding model ($•$). The error bar on the experimental data indicates the correlations between the spread in the energy of the reflectivity minima.

Figure 5

(a) Threshold image at $E-E_F=4.45$ eV with a $53\hspace{0.5em}\mu$m field of view showing clear intensity contrast due to work function variation across the surface. (b) Work function map of the FoV obtained from a pixel by pixel analysis of the threshold spectra. (c) Histogram of the work function values in (b) showing five distinct Gaussian distributions, corresponding to five distinct work function values.

Figure 6

(a) Local threshold spectra extracted from regions in Fig. 5b with work functions of 4.42 and 4.45 eV. The best complementary error function fits of the rising edge of the photoemission threshold are indicated by the solid line. (b) Second derivative smoothed threshold spectra from (a) showing peaks corresponding to the empty conduction band structure.

Figure 7

(a) Intensity map (arbitrary units) of the SiC substrate component of C1s spectrum after background subtraction. The darker regions correspond to lower intensity and therefore thicker graphene; FoV $53\hspace{0.5em}\mu$m. (b) The C1s intensities from graphene (squares) and from SiC (diamonds) as a function of work function.

Figure 8

C1s core level spectra extracted from the regions shown in Fig. 7 together with the best 5-peak fits. The vertical lines indicate the position of the peak attributed to the SiC substrate. The main graphene peak is light gray, the contamination peak is in black, and the SiC component is dark gray. The two other graphene peaks, labeled HBE-G and LBE-G, flank the main graphene peak. The thickness (calibration is described in the text) and work function are given for each spectra.

Figure 9

C1s graphene BE (squares), C1s SiC BE (diamonds), and work function (circles), as a function of graphene thickness. The unfilled symbols are for 1, 2, and 3 ML regions; filled symbols are for $1^{\prime }$ and $2^{\prime }$ ML regions. Open symbols with dots are for the $1^{″}$ ML.

Figure 10

(a) Experimental $I(k_x,k_y,E)$ data collected in the 2 ML region of Fig. 7. The principal and secondary Dirac cones at the $K$ and $K^{\prime }$ points of the first Brillouin zone are clearly visible. The secondary cones are rotated by $21.9^{°}$ with respect to the primary cones. Also evident is the already documented suppression of the photoemission intensity outside the first Brillouin zone due to the pseudospin structure when using $p$-polarized light. The tertiary cones are just visible inside the double hexagon defined by the principal and secondary cones. (b) Schematic of the Brillouin zone of graphene showing the two high-symmetry directions parallel and perpendicular to $\Gamma {\mathit{KM}}^{\prime }$ ($k_x$ and $k_y$, respectively) extracted from the $k$-PEEM data sets. An open source volume viewer, designed for medical imaging, was used to produce the image (Ref. 31).

Figure 11

Horizontal slice in the 3D $k$-PEEM data set of (a) 2 ML and (b) 3 ML at a binding energy of 1.3 eV. Secondary Dirac cones (graphene reciprocal lattice constant $g_1$) are rotated by $21.9^{°}$ with respect to the principal cones (graphene reciprocal lattice constant $g_2$). The tertiary cones are obtained by diffraction of either the secondary cone by the principal lattice vector $g_1$ (dotted line), or by the primary cone by the secondary lattice vector $g_2$ (dotted line). The tertiary cones are stronger in 2 ML graphene.

Figure 12

Band dispersion as a function of $k_y$ around the $K$ point at the first Brillouin zone boundary observed in the 3ML region for (a) principal and (c) secondary cones. The respective momentum distribution curves over the same energy range are shown in (b) and (d). The peak positions are highlighted by the dotted lines showing the variation in the position of the Dirac point for successive graphene layers.

Figure 13

Area averaged C1s core level spectrum. The average is over the $53\hspace{0.5em}\mu$m FoV.