Evaluation of transmission characteristics of CVD-grown graphene and effect of tuning electrical properties of graphene up to 50 GHz

Graphene has been investigated as a transparent conductive film for use in a variety of devices, and in recent years it has shown promise for use in millimeter-wave devices as 5G technology. In this study, we applied single-layer (SL), triple-layer (3L), and P-type doped 3L graphene to coplanar waveguide (CPW) transmission lines and obtained transmission characteristics (S21) from 1 to 50 GHz, which covered the 5G band. Furthermore, an equivalent circuit model of the CPW used in the measurements was constructed and simulations were performed, which showed good agreement with the measured results. The results validated the transmission properties of the graphene and the contact impedance at the interface between electrodes and the graphene in CPW circuits, which are necessary parameters for designing antennas using graphene. In addition, by comparing the transmission loss of three types of graphene, the parameters for improving the transmission characteristics were clarified.

doping up to 10 GHz 20 .While device applications of graphene in the terahertz band [21][22][23] have attracted much attention, there is insufficient research targeting the millimeter-wave region for 5G applications, which we aim to cover in our study.
In this report, we systematically evaluate the effects of graphene multilayering and carrier doping on transmission characteristics (S 21 ) from 1 to 50 GHz.Three types of graphene were fabricated: single-layer (SL), three-layer (3L), and P-type carrier doped 3L graphene with TFSA (Bis (trifluoromethanesulfonyl) amide) as the dopant, and their S 21 were measured.Furthermore, the electrical properties of graphene in the CPW were clarified by simulating the S 21 using the constructed equivalent circuit model of the CPW and comparing it with the measured S 21 of the CPW.The results clarified the behavior of three types of graphene in millimeter-wave devices such as its transmission characteristics and contact characteristics at the interfaces between graphene and electrodes, which are necessary parameter for designing antennas using graphene.

Results and discussions
In our study, SL, 3L, and P-type doped 3L graphene were fabricated to clarify how the transmission properties of graphene change with the number of layers and carrier doping.The fabrication of graphene and the devices for evaluation are described in the "Methods" section.
Optical transmittance in visible region.The optical transmittances in the visible region of the SL, 3L, and P-type doped graphene are shown in Fig. 1.Because a certain area (2 × 7 mm 2 ) is required to evaluate optical transmittance evaluation, three types of graphene (10 × 10 mm 2 ) were transferred to a quartz substrate and evaluated optical properties before forming the device.Furthermore, carrier doping was performed on 3L graphene before device fabrication, and the optical transmittance of P-type doped 3L graphene was evaluated.Note that the optical transmittance of the quartz substrate was subtracted for reference to discuss the optical properties of graphene only.As shown in Fig. 1, SL graphene showed the highest transmittance (97% at 500 nm).Graphene has an absorption of about 2.3% per layer in a visible wavelength region.Therefore, the transmittance of 3L graphene (89% at 500 nm) was lower than that of the SL graphene.Notably, P-type doped 3L graphene exhibited an optical transparency similar to pristine 3L graphene (90% at 500 nm).The P-type doping has the effect of increasing carrier density because it adds more holes, which is expected to improve conductivity 24 .Being able to improve electrical conductivity while maintaining optical transparency is a unique feature of graphene.
Raman spectra of graphene.The Raman spectra of the three types of graphene are shown in Fig. 2. The measurements were performed at the center of the graphene channels of the CPW devices.After evaluating the Raman spectra of 3L graphene, carrier doping was performed on the same sample to obtain the Raman spectra of P-type doped 3L graphene.G peaks at 1580-1600 cm -1 and 2D peaks at 2680-2700 cm -1 , which are characteristic of graphene, were observed as shown in Fig. 2a.For all samples, slight D peaks were observed at 1360-1370 cm -1 , which may be due to the defects induced during the transferring, stacking and fabricating the CPW processes.Significant damage was not observed with the optical microscope observation in Fig. S1.The intensity ratio of the 2D peak to the G peak in the Raman spectra (I 2D /I G ) correlate with the stacking structure of a multilayer graphene.The obtained I 2D /I G of the 3L graphene was 1.5, which is as high as that of SL graphene (I 2D /I G = 1.5).As shown in Fig. 2a, the full width at half maximum (FWHM 2D ) from fitting the 2D peak with the Lawrence function indicates that 3L graphene (FWHM 2D :35.2) is close to SL graphene (FWHM 2D :35.1).These suggested 3L graphene had a turbostratic stacking structure, which is characteristic of multilayer graphene obtained from a layer-by-layer process using polycrystalline graphene grown on polycrystalline Cu foils 10,18,25 .In general, the G peak of graphene originates from the in-plane motion of carbon atoms and shifts toward higher

Characterization of transmission characteristics (S 21 ) using CPW devices.
CPWs were used to evaluate the S 21 of graphene (Fig. 3a).A CPW consists of a signal line and ground lines and can be mounted on only one side of the board.Therefore, it is suitable for graphene evaluation because three-terminal probe measurements can be easily performed.CPWs with three types of graphene were fabricated by depositing Au as an electrode on the graphene samples and performing lithography.The characteristic impedance of the signal and ground lines was designed to have a characteristic impedance of 50 Ω 28 , with a signal line width of 400 µm and gaps of 36 μm between the signal line and ground lines.The graphene channel was formed to be 30 × 400 μm 2 (Fig. 3a,b).Note that graphene is under each of the signal and ground lines with Au.The S 21 of the fabricated CPW was measured from 1 to 50 GHz using a microwave probe (Form Factor, |Z| Probe GSG 500 μm) with guaranteed measurement range from DC to 50 GHz, a probe station (Form Factor, PM8), and a vector network analyzer (Keysight Technologies, E8361A) as shown in Fig. 3c,d.For the S 21 measurement, the CPW was connected to two ports of the vector network analyzer and input impedance of 50 Ω was extracted.After calibrating shorts, opens, loads, and throughs, the S 21 was measured.

Equivalent circuit model of CPW.
To analyze the contact impedance and the transmission characteristics of the graphene samples, an equivalent circuit model of the CPW was constructed as shown in Fig. 4 29,30 .The contact impedance between graphene and Au in the CPW transmission line was treated as a parallel circuit of contact resistance R contact and contact capacitance C contact .To prevent delamination of the Au electrodes in the probe measurement, the probe was contacted about 200 µm inside from both ends of the transmission line.For the frequency from 1 to 50 GHz, the areas between the probe contact position and the edge of the transmission line could act as an open stub, so the distance between the probe contacted area and the end of the transmission line was incorporated into the equivalent circuit as a transmission line with a characteristic impedance of 50 Ω (Fig. S2).
The graphene channel in the transmission line was expressed only in terms of frequency-independent impedance as R graphene .In the Drude model, the conductivity of graphene must take into account the frequency dependence associated with carrier scattering.This scattering follows an exponential relaxation time τ (0.01-2 picoseconds) depending on the mobility, Fermi level, and Fermi velocity 31,32 .The characteristic exponential relaxation time of τ = 2 picoseconds corresponds to ω/2π = 5.0 × 10 11 (500 GHz), which means that the resistor-capacitor (RC) network can be considered constant at least up to 500 GHz 33,34 .Furthermore, the skin effect of the conductor  www.nature.com/scientificreports/ is also frequency dependent.The thickness of the skin effect from typical CVD graphene conductivity (1.0 × 10 6 S/m) is 2.3-16 μm 35 from 1 to 50 GHz as calculated using the following equation, which is much thicker than 3L graphene, and the equivalent circuit model was constructed assuming that the frequency dependence of the impedance of the graphene channel in transmission line is negligible 36 .In parallel with R graphene , the parasitic capacitance generation between Au electrodes across graphene channel can also be accounted for, but it was not included in the equivalent circuit model because the electrode thickness (500 nm) is thin and the distance between electrodes across graphene channels (30 μm) in Fig. 3a is presumed to be greater than the distance between Au and graphene.
To assign the impedance such as R contact and R graphene of the equivalent circuit model (Fig. 4), experimental measurements were conducted using three types of graphene.
Impedance of R graphene .To determine R graphene , Hall effect measurements were performed on the three types of graphene using the van der Pauw method (Fig. 5a).Such properties can be measured without effects from the contact resistance.The results of the Hall effect measurements (Fig. 5b) are shown in Table 1.The carrier mobility of 3L graphene (2250 cm 2 /Vs) improved compared to that of SL graphene (1200 cm 2 /Vs).This suggests that graphene is less likely to be affected by carrier scattering effects from the quartz substrate due to multilayering 37 .The sheet resistance of graphene (R sheet ) was 758 Ω, 405 Ω, and 125 Ω for SL, 3L, and P-type doped 3L graphene, respectively.The carrier mobility (1090 cm 2 /Vs) of P-type doped 3L graphene decreased with TFSA doping, while the sheet resistance decreased with high carrier density (4.6 × 10 13 cm -2 ).A comparison of the carrier mobility of SL graphene (4.6 × 10 12 cm -2 ) and 3L graphene (6.8 × 10 12 cm -2 ) shows that carrier doping is effective in lowering resistivity.R graphene in the transmission line was determined from R sheet , taking into account the shape of the signal line of the CPW (Fig. 3a) as follows where W is the length (30 µm) and L is the width of the graphene channel in the transmission line (Fig. 3a).As shown in Table 1, the determined R graphene values were lowest for P-type doped 3L graphene (13 Ω) versus SL (42 Ω) and 3L graphene (78 Ω).
Contact resistance R contact .To obtain R contact between graphene and Au electrode, the transfer length method (TLM) was utilized as shown in Fig. 6.In the TLM results, the Y-axis intercept refers to 2R TLM between  www.nature.com/scientificreports/Au and the graphene [38][39][40] .The value of R contact was determined from the contact width between graphene and Au electrode (500 μm; Fig. 6) and the width between graphene and the Au electrode in the CPW (400 μm; Fig. 3a) as shown in Table 2. Kosuga et al. reported an R contact of 50 Ω for SL graphene using TLM 28 , which is not significantly different from our data (Table 2).The X-axis intercept of the straight lines in Fig. 6 represents the effective length (L t ) that contributed to the contact between the Au electrode and graphene.S t between the graphene and Au electrodes in the CPW circuit can be expressed as Where W is the width of the CPW signal line (400 μm).P-type doped 3L graphene exhibited an increase in St with P-type doping (5.3 × 10 -5 cm 2 ) as shown Table 2.This is based on the increase in the density of states (DOS) due to the lowering of the Fermi level, and as a result, P-type doped 3L graphene exhibited the lowest R contact value.
Contact capacitance C contact .C contact can be treated as a series circuit of the quantum capacitance of graphene (C q ) and the geometrical capacitance (C g ) between Au and graphene.
C q and C g can be obtained as follows [41][42][43] , where E F is the Fermi energy, v F is the Fermi velocity (1 × 10 8 cm/s), ħ is the reduced Planck's constant, and S t ' is the effective contact area between graphene and Au in the AC circuit.ε is the dielectric constant, and d corresponds to the distance between the electrode and graphene.Here, in the DC circuit, the effective contact area between graphene and Au (S t ) can be obtained from the TLM measurement.However, S t ' in the high-frequency band is difficult to determine because the current distributions in the CPW differ from that in DC measurements  www.nature.com/scientificreports/due to the current crowding and its frequency dependence.Therefore, C contact was treated as a fitting parameter in the analysis of S 21 , in which the measured S 21 is compared to the simulations.
Evaluation of S 21 .The electrical properties of the three types of graphene were reflected in an equivalent circuit model (Fig. 4) to simulate the S 21 .The simulations were performed using a 3D planar high-frequency electromagnetic software (Sonnet Lite 18.53), and after fitting C contact (Fig. S3), the transmission characteristics of graphene were evaluated by comparing them with the measured results.The C contact fitting was performed as shown in Fig. S3.The impedance of capacitance is shown below.
where f corresponds to frequency.The C contact fitting was performed at lower frequencies because C contact has a greater effect on contact impedance becomes large when the frequency is close to 1 GHz.Fig. S3 shows that the S 21 calculation results were close to the measured values and saturated when the C contact is above 200 pF for SL and 3L graphene and above 1 nF for P-type doped 3L graphene.From the results, the value of C contact of three types of graphene could not be uniquely determined.Therefore, for the S 21 calculations, the C contact of SL and 3L graphene was regarded as 200 pF and the C contact of P-type doped 3L graphene was treated as 1 nF.Our findings suggest that the larger C contact of P-type doped 3L graphene is due to the increase in quantum capacitance (C q ) resulting from the increase in carrier density (Table 1).Hence, the value of C contact may have changed as the value of C q increased.This indicates that the values of C q and C g are comparable.
Figure 7a shows the magnitude of S 21 versus frequency.Comparing the magnitudes of the three types of graphene, the transmission loss decreased in the order of SL, 3L, and P-type doped 3L graphene.The transmission loss was smaller with lower values of the R graphene in the graphene channel (Fig. 3a), indicating that the multilayering and carrier doping of graphene are effective for reducing the transmission loss.www.nature.com/scientificreports/ Figure 7b shows the experimental and calculated results of the S 21 of the CPW in a polar chart.The polar coordinates represent the Real part on the X-axis and the Imaginary part on the Y-axis, and can be obtained from the magnitude and phase of S 21 by the following equation.Hence, the phase and magnitude can be compared from the polar chart.
Because the maximum value of magnitude is 0 dB, the X and Y-axes of the polar chart take values from -1 to 1. Here, magnitude and phase can be converted using the following equation.
The magnitude increases when the Real and Imaginary parts are large.In other words, when the value of Real and Imaginary are far from the origin in the polar chart, it means that the transmission loss is small.As shown in Fig. 7b, for both graphene samples, the calculated and experimental values were in close agreement from 1 to 50 GHz.These results indicate that both the magnitude and the phase were accurate, thus validating the design policy of this equivalent circuit model.Furthermore, the results indicate that the impedance of graphene channel in the CPW (Fig. 3a) can be expressed only in terms of resistance from 1 to 50 GHz frequency, as discussed in the previous section.It is also demonstrated that the introduction of open stubs brings the measured values closer to the calculated values in Fig. S4, and the open stubs was necessary for the equivalent circuit model.
The Au and graphene contacts of the CPW used in this study ware represented by a parallel circuit of R contact and C contact .Figure 8 shows the calculation and comparison of the impedance of R contact and C contact versus frequency.In the frequency range from 1 to 50 GHz, the impedance of C contact is clearly smaller, indicating that the contact impedance is dominated by capacitance 10 .Awan et al. 's study 29 , which was used as a reference for constructing the equivalent circuit model, evaluated the transmission characteristic of CPW with SL graphene but did not assume that capacitance is the dominant factor in contact impedance.The value of C contact in Awan et al. 's experiment was set at 0.12 pF, which is smaller than our value (C contact > 200 pF).This is because the contact area between the Au electrode and graphene in our study (Fig. 3a) is larger than in Awan et al. (100 μm 2 ).Thus, these results indicated that the large contact area between the Au and graphene enabled the C contact to be the dominant factor in the contact impedance.
Our research clarified the transmission characteristics of graphene for the 5G frequency by experimentally measuring the S 21 of the CPW using the graphene at 1 -50 GHz and comparing them with the constructed equivalent circuit model of the CPW.To our knowledge, our study is the first compare the S 21 of various graphene materials with different electrical properties while maintaining transparency.From this comparison, we found that the graphene channel in the CPW can be expressed only in terms of resistance.In addition, multilayering and carrier doping are effective in reducing transmission loss of the graphene, and the contact impedance can be reduced by increasing the contact area between Au and graphene.These are important findings for the design of transparent 5G antenna devices using graphene.
It is evident that graphene will continue to be studied to lower resistivity, increase mobility, and enable processes for larger area, toward a variety of device applications.Our study is one step in that direction, and it has www.nature.com/scientificreports/provided valuable insights not only for designing transparent 5G antennas with graphene but also for the design of other devices such as microwave ring resonators, absorber, photodetectors, and terahertz devices using the graphene.

Conclusion
We have fabricated CPWs using three types of graphene and measured the S 21 from 1 to 50 GHz.We also measured the optical and electrical characteristics of the three types of graphene, built equivalent circuit models, and calculated.The agreement between the simulated S 21 and measured S 21 supports the validity of the constructed equivalent circuit model, in addition, the contact impedance value and the transmission loss of graphene channel were clarified.The comparison of the S 21 of the three types of graphene shows that carrier doping and multilayering of graphene are effective in reducing transmission loss while maintaining the transparency of graphene in the operated 5G frequency.The results provide design guidelines for the introduction of graphene as a transparent conductive material in 5G antennas to replace existing materials such as meshed Cu, metal nanowires, and ITO films.Increasing the contact area between Au and graphene was also found to be effective in reducing contact impedance.In designing 5G antennas, it is important to connect the device to the power feed with minimal losses, and our experimental results show that a large contact area between the graphene and electrode is an important consideration as it reduces contact losses.
Our findings provide insights into the design of millimeter-wave devices using graphene and, furthermore, provide the basis for the application of graphene as a radiating element of transparent 5G antennas.

Methods
Figure 9 shows a series of processes from graphene growth to device fabrication.

CVD growth and graphene stacking.
To grow graphene as a uniform monolayer, Cu foil was selected as a catalyst substrate.Before graphene growth, the Cu foil was annealed at 1000 °C for 30 min in H 2 (20 sccm) atmosphere for cleaning.Graphene was grown by low-pressure CVD on the Cu foil using H 2 and CH 4 gas.The CVD growth proceeded for 30 min under H 2 (20 sccm) and CH 4 (2 sccm) flows at 1000 °C.For transfer processes, PMMA (Aldrich, M.W. = 996,000) in an ethyl lactate solution (4 wt%) was spin-coated onto graphene as a supporting layer and cured at 180 °C for 1 min.
The PMMA was wiped off with acetone during spin-coating because it also spread around to the back side of Cu foil.In the CVD process, graphene grew on both sides of the Cu foil, causing subsequent Cu etching failure.Therefore, oxygen plasma treatment (O 2 :30 sccm, power: 20 W, time: 60 s) was performed on the opposite side of the Cu foil from the side where the PMMA film was formed to remove the unwanted graphene.Then the PMMA coated SL graphene sheet was obtained by etching the Cu foil.To form SL graphene on a substrate, the PMMA-coated SL graphene sheet (size: 10 × 10 mm 2 ) was transferred onto a quartz substrate (size: 20 × 20 mm 2 , thickness: 1 mm), and the PMMA was removed by immersing it in an acetone for 12 h.The 3L graphene samples were obtained by a layer-by-layer process in which a PMMA-coated SL graphene sheet was repeatedly transferred to another graphene grown on a Cu foil sample.The rest of the process was the same as that for fabricating SL graphene: etching Cu, transferring to the quartz substrate, and removing PMMA to obtain the 3L graphene on the quartz sample.

Figure 5 .
Figure 5. (a) Design and (b) image of Hall effect measurement.

Figure 6 .
Figure 6.TLM for three types of graphene.

Table 1 .
Results of Hall effect measurement of three types of graphene.

Table 2 .
R contact of three types of graphene obtained from TLM measurements.