Graphene features in spectroscopy and estimation of the graphene

Figure 7.6 | Point spectroscopy. (a)dI/dV spectroscopy on G/Au(111) and on pure Au(111) for Auhcpand Aufcc sites. (b)The onset of the Au surface state can be derived from the difference between the Auhcpand Aufccspectroscopy leading to the values ofE_0,Au= -0.43 eV andE_0,G/Au= -0.32 eV. Parameters for spectroscopy:V_stab=0.5 V,I_stab=200 pA,V_mod=3 mV,T₌8.3 K

film thickness and shows slight variations (±50 meV) across the sample.

The dispersion relation extracted from the graphene covered area also shows a para-bolic dispersion relation with fit parametersE0,G/Au =(−0.30±0.03) eV and m^∗_G/Au = (0.26±0.02)me. A clear shift towards lower binding energy of∼100 meV is apparent and explains the difference in standing wave periodicities measured in Figure 7.1 (b). The comparable effective mass suggests the measured scattering to arise from the surface state of the underlying metal, which decays exponentially into vacuum [165] and can survive underneath a weakly interacting graphene layer [245]. A simple shift of the sur-face state has been previously reported for noble gases adsorbed on the Au(111) sursur-face [246], for molecules on Au(111) [247] and also for graphene on Ir(111) [142].

7.1.3 Graphene features in spectroscopy and estimation of the graphene binding energy

The point spectroscopy performed on G/Au(111) and Au(111) corroborates the observed shift of the surface state. Local point spectroscopy on Au(111) surfaces was shown to give valuable information on the surface state onset. In Figure 7.6 (a) dI/dV spectra ac-quired locally on the Auhcp(solid cyan line) and Aufcc(dashed cyan line) regions of the herringbone reconstruction are depicted [compare Figure 6.7 for a representation of the herringbone reconstruction sites]. The two spectra both feature similar behavior except for an energy range around−0.4 eV. Chenet al.showed that the additional super-lattice potential of the herringbone reconstruction leads to a localization of low energy

electrons at Auhcpsites thus increasing the DOS at energies at the bottom of the band.

Electrons react to this imbalance by localizing at the Aufccregions for higher energies [248]. The difference between spectra at Auhcpand Aufccpositions was found to form a sharp peak at an energy which is characteristic for the surface state onsetE0. The differ-ence between the dI/dV signal of Auhcpand Aufccregions on the investigated Au(111) surface is depicted in Figure 7.6 (b) and displays a clear peak which allows to define the energy minimum of the surface state toE0,Au= −0.43 eV. The energy minimum is in good agreement with the value extracted from the fitting procedure of dispersion rela-tionsE(k).

Performing the same spectroscopy experiment on graphene, again distinguishing between the herringbonefccandhcpregions of the underlying Au surface, yields similar dI/dV curves. The energy onset of the surface state appears shifted toE0,G/Au= −0.32 eV compared to pure Au(111). This shift corresponds to the observed energy shift of the surface state of Au underneath graphene with reasonable accuracy. From a number of different measurements on various samples the shift of the surface state can be inferred to be∆E0=100±10 meV.

Characteristic graphene features in STS spectra, such as a V-shaped DOS, are not found in the acquired data. Instead, graphene appears to be virtually transparent to the STS experiment presented here, both in dI/dV(V) spectra and in dI/dV maps. De-spite the lack of graphene features in these measurements, the shift of the surface state allows for an estimation of the adsorption energy of the graphene on Au(111). It has been pointed out that Shockley type surface states are sensitive probes for adsorption processes, which lead to an empirical linear dependence of the adsorption energy from the surface state shift based on experiments with noble gases and molecules [247]. The absorption energy per area Eads depends on the surface state shift ∆E via a propor-tionality constant of 0.106 Å⁻². In the case of graphene on Au(111) this corresponds to E_ads=0.106 Å⁻²∆E = (10.6±1) meV/Ųor to an adsorption energy of 56±6 meV per unit cell. A comparison to binding energies of graphene from DFT yields reasonable agree-ment, however it has to be treated with caution, since different functionals show varying binding characteristics [249, 250]. In the case of G/Au(111) the local density approxi-mation yields a binding energy per atom of 31 meV [249] comparable to the findings extracted from the Shockley surface state shift (2 atoms per graphene unit cell). Includ-ing the non-local van-der-Waals corrections within the vdW-DF functional still leads to a fairly reasonable value with a slightly increased binding energy of 38 meV per atom [249].

Conclusion

The clear parabolic behavior of the dispersion relations observed both on G/Au(111) and on Au(111) suggest that the observed modulations of LDOS are solely due to the surface state of the Au(111) substrate. A simultaneous existence of confined graphene electrons and surface state electrons cannot be inferred from this kind of measurements.

Fur-7.1 Surface state electrons 113

thermore the local point spectroscopy shows no sign of graphene DOS and suggests that graphene is virtually transparent to the particular tip used in the measurements pre-sented in this section. On the other hand, the adsorption energy of graphene on Au(111) appears to be comparably low, only slightly larger than Ar or Kr gases physisorbed on the Au(111) surface. Based on the method of Ziroffet al.[247] an adsorption energy of 56±6 meV is extracted indicative of a negligible interaction of graphene with the sub-strate.

7.2 Dispersion relations of single and double layer graphene