TheRg , Lg ,Rc , and Cc , which were
determined in the previous section, are listed in Table I. The
reflection coefficients for the equivalent circuit model were calculated
using these parameters. Figure 3 shows the measured (solid lines) and
calculated (dashed lines) reflection coefficients of the CPWs from 1 to
15 GHz on a smith chart. The red, blue, and green lines correspond to
the data of the reflection coefficients for CPWs with the graphene lines
of L =10, 30, and 50 μm. The points in Figure 3 are the measured
and calculated reflection coefficients at 5, 10, and 15 GHz. As shown in
Figure 3, the reflection coefficients depended on L . The
calculated reflection coefficients for this model nearly agreed with the
measured ones from 1 to 15 GHz. Therefore, this model can be applied for
the analyzing the contact properties between metal and graphene up to 15
GHz. The phase angle of the reflection coefficients for the graphene
lines of L =50 μm was smaller than that for graphene lines ofL = 10 μm. We previously reported that the phase constant\(\text{β\ }\left(\approx\frac{1}{2}\omega\mu_{0}\sigma\right)\ deg/mm\)of graphene is smaller than that of metal due to the lower conductivity\(\sigma\) of graphene [9]. Therefore, the \(\beta\) of the graphene
line decreases with increasing L . Consequently, the contact
impedance was correctly characterized by Rc andCc obtained from the TLM, Hall measurement, and
estimation, as shown in
Table
I.
We presented the contact impedance at the interface between a metal and
graphene from 1 to 15 GHz. As mention the above,Rc and Cc were 50 Ω and
2.2 nF, respectively. In Figure 4 (a), the impedance ofCc is plotted as a function of frequency. It
should be that the the impedance of Cc is
represented as \(|\frac{1}{\omega C_{c}}|\) and is more than two orders
of magnitude lower than that of Rc from 1 to 15
GHz. It also should be noted that the contact impedance consists ofRc and Cc . Therefore,
these results indicate that the current flows mainly not throughRc , but through Cc in the
microwave band. In the DC band, houwever, most of the current flows
through Rc because the impedance value ofCc is approximately infinite. Therefore, it is
suggested that the current flow from a metal into graphene in the
microwave band is more capacitive and efficient than that in the DC
band. In Figure 4 (b), the ratio of power consumption and power storage
in the microwave band Pmw , to the total power
consumption in the DC band Pdc , which represents
the degree of energy dissipation at the metal/graphene contact, is
plotted as a function of Cc . ThePmw /Pdc ratio is expressed
as\(\frac{P_{\text{mw}}}{P_{\text{dc}}}=\frac{|\frac{1}{\omega C_{c}}|}{R_{c}+|\frac{1}{\omega C_{c}}|}\times 100\ [\%]\).
The black, blue, and red lines correspond to thePmw /Pdc ratio for 5, 10,
and 15 GHz, respectively. ThePmw /Pdc ratio decreased
with increasing frequency and incresing Cc .
Therefore, in the microwave band, Cc is a
critical factor, hence, a reduction in the impedance ofCc should be achieved for more efficient carrier
injection from metal to graphene. These results indicate that a higherCc is preferred in designing the feeding
structure of graphene-based microwave devices such as antennas and
transmission lines. For example, a larger contact area leads to a higherCc because of increasing ST.
Furthermore, increasing the n of graphene may provide a higherCc because it is represented byCq of graphene, which is proportional ton .
Conclusions
The contact properties at the interface between metal and graphene in
the microwave band from 1 to 15 GHz were analyzed through experimental
measurements and caluculation with an equivalent circuit model using
lumped circuit components. The calculated reflection coefficients based
on the lumped circuit components nearly agreed with the measured ones,
which indicated that the equivalent circuit model can be applied to
analyze the contact properties between metal and graphene up to 15 GHz.
The impedance of Cc was more than two orders of
magnitude lower than that of Rc . This indicates
that most of the carrier injection from metal to graphene flows not
through Rc but through Ccin the microwave band, which suggests that the current flow between
metal and graphene in the microwave band is more capacitive and
efficient than that in the DC band. Therefore, the interface between
metal and graphene with high capacitance is preferred in designing the
feeding structure of graphene-based microwave devices. This work
provides a building block that is essential for designing optically
transparent graphene-based antennas.
- Figure legends Figure 1: (a) Bird’s eye and
cross-sectional views and (b) equivalent circuit model of fabricated
CPWs.
Figure 2: Measured resistance extracted with
TLM. Inset is schematic structure of TLM
device.
Figure 3: Measured (solid) and calculated
(dashed) reflection coefficients with graphene lines of L = 10 (red),
30 (blue), and 50 μm (green) on smith chart. Points on graph are
reflection coefficients at 5, 10, and 15 GHz.
Figure
4: (a) Impedance of parallel contact resistanceRc . and contact capacitanceCc . (b) Ratio of power consumption and power
storage in microwave band Pmw to total power
consumption in DC band Pdc for 5 (black), 10
(blue), and 15 GHz (red).
Table I: Measured and
estimated parameters of CPWs.
- Acknowledgements This work was supported by JSPS KAKENHI (19J14640, 19K05218, and
20H02209), Aoyama Gakuin University-Supported Program “Early Eagle
Program”, and Nippon Sheet Glass Foundation Material Science and
Engineering.
- Ethic statement We do not violate ethics.
- Conflict of Interests Authors have no conflict of interest relevant to this article.
- Literature cited [1] Guan N., Furuya H., Himeno K., Goto K., and Ito K. Basic study
on an antenna made of a transparent coductive film. IEICE Trans
Commun. 2007;E90-B(9):2219-2224.
[2] Green R. B., Toporkov M., Ullah M. D. B., Avrutin V., Ozgur
U., Morkoc H., Topsakal E. An alternative material for transparent
antennas for commercial and medical applications. Microwave Opt
Technol Lett. 2017;59:773-777.
[3] Lee C. M., Kim Y., Kim Y., Kim I. K., Jung C. W. A flexible
and transparent antenna on a polyamide substrate for laptop computers.Microwave Opt Technol Lett. 2015;57:1038-1042.
[4] Clasen G. and Langley R. Meshed patch antennas. IEEE
Trans Antennas Propag. 2004;52:1412
[5] Lin Y. M., Valdes-Garcia A., Han S. J., Farmer D. B., Meric
I., Sun Y., Wu Y., Dimitrakopoulos C., Grill A., Avouris P., Jenkins
K. A. Wafer-scale graphene integrated circuit. Science.2011;332:1294-1297.
[6] Nair R. R, Blake P., Grigorenko A. N., Novoselov K. S., Booth
T. J., Stauber T., Peres N. M. R., Geim A. K. Fine structure constant
defines visual transparency of graphene. Science.2008;320:1308.
[7] Kim K. S., Zhao Y., Jang H., Lee S. Y., Kim J. M., Kim K. S.,
Ahn J-Y, Kim P., Choi J-Y, Hong B. H. Large-scale pattern growth of
graphene films for stretchable electrodes. Nature.2009;457:706-710.
[8] Kosuga S., Suga R., Hashimoto O., Koh S. Graphene-based
optically transparent dipole antenna. Appl Phys Lett.2017;110:233102.
[9] Kosuga S., Suga K., Suga R., Hatanabe T., Hashimoto O., Koh S.
Radiation properties of graphene-based optically transparent dipole
antenna. Microwave Opt Technol Lett. 2018;60:2992-2998.
[10] Grande M., Bianco G.V., Laneve D., Capazzuto P., Petruzzeli
V., Scalora M., Prudenzano F., Bruno G., D’Orazio A. Optically
transparent wideband CVD graphene-based microwave antennas. Appl
Phys Lett. 2018;112:251103.
[11] Yi D.,Wei X. C., Xu Y. L. Tunable microwave absorber based on
patterned graphene. IEEE Trans Microw Theory Tech.2017;65:2819-2826.
[12] Grande M., Bianco G. V., Vincenti M.A., Ceglia D.D.,
Capezzuto P., Petruzzelli V., Scalora M., Bruno G., D’Orazono A.
Optically transparent microwave screens based on engineered graphene
layers. Opt Express. 2016;24:22788-22795
[13] Huang X., Leng T., Zhu M., Zhang X., Chen J. C., Chang K. H.,
Aqeeli M., Geim A. K., Novoselov K. S., Hu Z. Highly flexible and
conductive printed graphene for wireless wearable communications
applications. Sci Rep. 2016;5:18298.
[14] Sajal S., Braaten B. D., Travis T., Asif S., Schroeder M. J.
Design of a coformal monopole antenna on a paper substrate using the
properties of graphene-based conductors. Microwave Opt Technol
Lett. 2016;59:1279-1183.
[15] Nagashio K. and Toriumi A. Density-of-states limited contact
resistance in graphene field-effect transistors. Jpn. J. Appl.
Phys. 2011;50:070108.
[16] Skulason H. S., Nguyen H. V., Guermoune A., Sridharan V.,
Siaj M., Caloz C., Szkopek T. 110 GHz measurements of large-area
graphene integrated in low-loss microwave structures. Appl Phys
Lett. 2011;99:153504.
[17] Jeon D-Y, Lee K. L., Kim M., Kim D. C., Chung H-Y, Woo Y-S,
Seo S.
Radio-Frequency Electrical Characteristics of Single Layer Graphene.Jpn. J. Appl. Phys. 2009;48:091601.
[18] Nagashio K, Nishimura T, Toriumi A. Estimation of residual
carrier density near the Dirac point in graphene through quantum
capacitance measurement. Appl Phys Lett. 2013;102:173507.
[19] Schroder D. K. Semiconductor Material and Device
Characterization. Danvers, USA: John Wiley & Sons; 1998.
[20] Wong H. P. Carbon Nanotube and Graphene Device
Physics. New York, USA: Cambridge University Press; 2011.