The Rc was experimentally determined from the transfer length method (TLM) test using the TLM device structure shown in the inset of Figure 2. The TLM device consists of a monolayer CVD graphene strip and Au electrodes. The width of the graphene strip was fixed to 0.5 mm, and the distances between the two adjescent Au electrodes were set to 0.1, 0.15, 0.2, 0.25, and 0.3 mm. The contact area between the graphene strip and Au electrodes were set to\(0.1\times 0.5\ \text{mm}^{2}\). In Figure 2, the measured resistance, including the channel resistance and contact resistances, of the graphene strip are plotted as a function of the length of the graphene strip, and the red line is the linear fitting line. For zero distance, the channel resistance vanished and the intersection point of the resistance axis corresponded to the contact resistances 2Rc (~ 80 Ω). Thus, the contact resistance in the TLM device was estimated to be 40 Ω. The contact resistivity depends on the contact width between the graphene and electrodes; hence, it can be calculated as 20 Ω mm. Since the width of the graphene lines, \(W\), of the CPWs was fixed to 400 μm, the contact resistance in the CPWs was estimated to be 50 Ω.
The Cc was estimated considering the transfer area ST [cm2] underneath the Au layer and the quantum capacitance per unit areaCq nF/cm2 of the monolayer CVD graphene in the CPW. The Cc can be expressed as\(C_{c}=C_{q}\times S_{T}\) nF. At the interface between Au and graphene, current crowding takes place in the effective\(S_{T}=d_{T}\times W\), where dT is the transfer length at the interface between Au and graphene. ThedT , which can be determined as the interseption point of the distance axis in Figure 2, was ~80 μm [19]. Since W was fixed to 400 μm, \(S_{T}\) can be calculated as 3.2×10-4 cm2. Nagashio et al. reported that the Cq of graphene is proportional to the Fermi energy of graphene [18] and can be expressed as
\begin{equation} C_{q}=\frac{2e^{2}E_{F}}{\pi\left(v_{F}\hslash\right)^{2}},\nonumber \\ \end{equation}
where EF is the Fermi energy,vF is the Fermi verocity (\(1\times 10^{8}\ cm/s\)) and \(\hslash\) is Plank’s conatant. TheEF are given by
\begin{equation} E_{F}=\hslash v_{F}\sqrt{\frac{n\pi}{\lambda}},\nonumber \\ \end{equation}
where n is the carrier density of graphene and \(\lambda\) is the fitting parameter, which is generally set to 1.1 [20]. Since the measured sheet carrier density of the monolayer CVD graphene is 6.4×1012 cm-2, theEf of the monolayer CVD graphene can be calculated as ~0.28 eV. Therefore, theCq of graphene can be estimated from the above equation to be 6.7 μF/cm2. Consequently,Cc can be calculated as 2.2 nF using\(C_{c}=C_{q}\times S_{T}\).
Discussion on contact impedance