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