Figure 1 (a) shows the structure of one of the CPWs fabricated using monolayer CVD graphene and Au on a quartz glass substrate. Note that the graphene layers lie underneath all areas of the Au layers. In the area of monolayer CVD graphene, the width of the graphene linesW was fixed 400 μm and the lengthes of the graphene linesL were set to 10, 30, and 50 μm. The characteristic impedance of an Au CPW is 50 Ω and the length of the CPW is 4000 μm. The signal line width is 400 μm and the gap between the signal line and ground is 36 μm. Graphene layers were grown on Cu foils by low-pressure CVD and transferred onto the quartz glass substrate. A CPW composed of graphene and Au was fabricated by electron beam evaporation and standard photolithography. The detailed fabrication procedure of the CPWs were reported in a previous paper [8].

The reflection coefficients of the fabricated CPWs were measured from 1 to 15 GHz using a ground-signal-ground microwave probe on a wafer-probe station and a vector network analyzer. One port of the vector network analyzer was connected to one of the fabricated CPW. The terminal of the fabricated CPW was an electrical open. The measured reflection coefficients will be shown and discussed later.

The contact characteristics of the metal/graphene contact were analyzed using the equivalent circuit model shown in Figure 1 (b). There are three components to this model: an Au-based CPW with characteristic impedance, contact impedance, and impedance of the graphene line. The contact impedance is represented by R_c andC_c . We assumed that the characteristic impedance of the CPW fabricated using Au/graphene is 50 Ω because the contribution of the graphene underneath the Au layers is negligible and thatC_c is represented by the quantum capacitanceC_q of graphene [18]. The graphene line impedance is represented by the series resistanceR_g and series inductanceL_g of the graphene line [17]:L_g is the kinetic inductance of the graphene line. It was assumed that the graphene impedance and contact impedance can be represented by lumped circuit components because L is much smaller than the electrical length from 1 to 15 GHz.

To quantitavely characterize R_g , we processed the monolayer CVD graphene film into a Hall bar device of a van der Pauw geometry placed on a quartz glass substrate. Hall measurements provided electrical properties, such as the sheet resistance, carrier mobillity, and carrier density of the graphene film, which are not affected by the contact resistance [19]. The measured sheet resistance, carrier mobillity, and sheet carrier density of the monolayer CVD graphene are 750 Ω/sq, 1,320 cm²/Vs and 6.4×10¹²cm^-2, respectively. The Hall coefficient is postive (+98 m²/C), inidicating that the charge carriers in the grpahene chanel are holes. According to the measured sheet resistance of the monolayer CVD graphene, the R_gfor the graphene lines of L =10, 30, and 50 μm in the CPWs can be calculated to as 19, 56, and 93 Ω, respectively.

The sheet impedance of graphene, \(Z_{s}\ \Omega/sq\), can be expressed as \(Z_{\text{sq}}=R_{\text{sq}}+j\omega L_{\text{sq}}\), whereR_sq and L_sq are the sheet resistance and sheet inductance of graphene, respectively. It should be noted that the units of R_sq andL_sq are defined as \(\Omega/sq\) and\(H/sq\ \)(\(=\Omega s/sq\)). Jeon et al. reported thatL_sq can be expressed as\(L_{\text{sq}}=\text{τR}_{\text{sq}}\), where \(\tau\) is the transport relaxation time, which was assumed to be 1 ps in a previous report [17]. We also assume that \(\tau\) is 1 ps andR_sq is determined to be 750 \(\Omega/sq\) in the Hall measurement. Thus, L_sq in the graphene line in this study was estimated to be about 0.75 nH/sq. Therefore, theL_g for the graphene lines of L =10, 30, and 50 μm in the CPWs can be calculated as 0.019, 0.056, and 0.093 nH, respectively.