# Reduction of Schottky Barrier Height at Graphene/Germanium Interface with Surface Passivation
## 4 Discussion  
From the position of the main Ge3d peak, we can determine the Schottky barrier height for electrons, defined as the difference in energy between the Fermi level and the conduction band minimum at the interface, with the following equation:  
\[\phi_{B}=\left(\Delta(VB-Ge3d)+E_{g}\right)-BE^{Ge3d} \tag{1}\]  
where \(\Delta(VB-Ge3d)\) is the energy difference between the Ge3d core level and the valence band, \(E_{g}\) is the Ge bandgap and \(BE(Ge3d)\) is the measured binding energy of the Ge3d core level referenced to the Fermi level. \(\Delta(VB-Ge3d)\) is set to 29.30 eV [25] and the Ge bandgap to 0.67 eV. The measured SBHs are summarized in Table 1 as a function of the surface treatment. Table 1 summarizes the SBH of our heterostructures with different surface treatments with and without graphene and before and after Au deposition. We can notice that the SBH of intimate Au/Ge interfaces is independent of the Ge surface treatment. These SBH values are close to previous reports for Au/Ge contacts [34]. For metal/Ge interfaces, the FL is strongly pinned close to the valence band \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Surface Treatment** & **G/Ge** & **Au/G/Ge** & **Au/Ge** \\ \hline HF & 0.49 & 0.53 & 0.78 \\ HCl & 0.31 & 0.50 & 0.77 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Schottky Barrier Height (in eV) for various Ge surface treatments. Figure 3: C1s core level of the graphene-covered regions for HF- and HCl-passivated Ge surfaces before and after 1 nm Au deposition. edge. Indeed the SBH only weakly depends on the metal work function ranging from 0.49 to 0.67 eV for metal work functions variations of 2.8 eV [35]. The introduction of a graphene monolayer between Au and Ge strongly reduces the SBH to about 0.5 eV. This behavior suggests that the FL pinning was alleviated by the presence of graphene at the interface. An even lower SBH value of 0.31 eV was obtained for graphene on a HCl-treated Ge surface. This is a strong indication that the chloride passivation was efficient in reducing the surface state density and that the FL is not pinned. In that case, we can apply the simple model of Schottky-Mott where the SBH \(\phi_{\rm B}\) is:  
\[\phi_{\rm B}=W_{\rm G}-\chi_{\rm Ge} \tag{2}\]  
with \(W_{\rm G}\) the work function of graphene and \(\chi_{\rm Ge}\) the electronic affinity of the semiconductor. [PERSON] et al. [36] measured a \(W_{\rm G}\) of 4.3 eV for CVD-graphene deposited via a PMMA-assisted method similar to ours. This value is lower than the commonly used 4.54 eV because of resist contamination and structural defects induced during wet transfer. With an electron affinity of 4.0 eV for Ge, this would lead to an SBH of 0.30 eV, in excellent agreement with our result. For an un-passivated surface, the FL is expected to be pinned close to the charge neutrality level (0.09 eV above the valence band maximum [35]). In that case, [PERSON] et al. [35] predict an SBH of 0.56 eV for a graphene/Ge contact. The SBH for G/Ge:H is between these two values, suggesting a less efficient passivation of HF compared to HCl. This is expected since the hydrogen passivation is not stable in air and hydrogen is removed from the surface within a few minutes [37]. [PERSON] et al. [38] showed on G/Si:H that the dominant interaction between graphene- and hydrogen-passivated Si surfaces is through Van der Waals forces. In that case, C and Si atoms do not interact with each other. Depassivation of Si induced a stronger interaction between Si and C atoms, eventually leading to the formation of covalent bonds and an increased density of states in the gap of Si. The situation is similar here, with a weak interaction between C and Ge atoms associated with a low density of states in the Ge bandgap when passivation is efficient (Cl-passivation). When the passivation is less efficient (H-passivation), the interaction between C and Ge atoms becomes stronger and the density of states in the Ge gap increases. As gold is deposited on the G/Ge:Cl surface, the SBH increases by 0.19 eV.