Characterization of CVD graphene permittivity and conductivity in micro /millimeter wave frequency range Yunqiu Wu, Yun Wu, Kai Kang, Yuanfu Chen, Yanrong Li, Tangsheng Chen, and Yuehang Xu Citation A[.]
Characterization of CVD graphene permittivity and conductivity in micro-/millimeter wave frequency range Yunqiu Wu, Yun Wu, Kai Kang, Yuanfu Chen, Yanrong Li, Tangsheng Chen, and Yuehang Xu Citation: AIP Advances 6, 095014 (2016); doi: 10.1063/1.4963140 View online: http://dx.doi.org/10.1063/1.4963140 View Table of Contents: http://aip.scitation.org/toc/adv/6/9 Published by the American Institute of Physics Articles you may be interested in Compression of Hamiltonian matrix: Application to spin-1/2 Heisenberg square lattice AIP Advances 6, 095024095024 (2016); 10.1063/1.4963834 Kinetic Monte Carlo of transport processes in Al/AlOx/Au-layers: Impact of defects AIP Advances 6, 095112095112 (2016); 10.1063/1.4963180 Quantization of time-dependent singular potential systems: Non-central potential in three dimensions AIP Advances 6, 095110095110 (2016); 10.1063/1.4962995 Theoretical study of CO and O2 adsorption and CO oxidation on linear-shape gold molecules (LGMn) (n=2, 4, 8, 16, and 24) AIP Advances 6, 095206095206 (2016); 10.1063/1.4962824 AIP ADVANCES 6, 095014 (2016) Characterization of CVD graphene permittivity and conductivity in micro-/millimeter wave frequency range Yunqiu Wu,1 Yun Wu,2 Kai Kang,1 Yuanfu Chen,3 Yanrong Li,3 Tangsheng Chen,2 and Yuehang Xu1,3,a School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China Science and Technology on Monolithic Integrated Circuits and Modules Laboratory, Nanjing Electronic Device Institute, Nanjing 210016, People’s Republic of China State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, People’s Republic of China (Received 17 May 2016; accepted September 2016; published online 15 September 2016) The permittivity and conductivity of chemical vapor deposited monolayer graphene are investigated up to 40 GHz The characterization method is based on a coplanar waveguide transmission line structure that is fabricated on a multilayer substrate of Si/SiO2 /graphene/Al2 O3 from the bottom up The effective relative permittivity of the coplanar waveguide transmission line is extracted using Thru-Reflect-Line calibration and scattering parameter measurements, and then the relative permittivity and corresponding conductivity of graphene are characterized using partial capacitance techniques The results demonstrate that the conductivity and sheet resistance are remarkably frequency-dependent and that the complex relative permittivity is consistent with the Drude model © 2016 Author(s) All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/) [http://dx.doi.org/10.1063/1.4963140] Two-dimensional (2D) materials have recently drawn tremendous attention for emerging electronics Among these 2D materials, graphene has shown great potential in micro-/millimeter wave applications due to its superior mobility.1 The accurate characterization of the permittivity and conductivity of graphene in a broad frequency band is the basis of high-frequency graphene integrated circuit (IC) design As a result, the characterization of graphene’s properties in the micro-/millimeter wave range is important for the development of all-graphene or graphene/Si hetero-ICs.2,3 One characterization method is based on a lumped element model In 2009 and 2011, Deligeorgis et al reported a lumped element model for the exfoliated graphene flakes under coplanar waveguide (CPW) transmission lines up to the W-band.4,5 In 2013, Mircea Dragoman et al investigated a graphene CPW coupled line and extracted the effective permittivity up to 40 GHz.6 In 2014, Rahim et al compared several on-wafer calibration methods and improved the measurement accuracy of graphene transmission lines.7 In 2015, Mingguang Tuo et al discussed the linear and nonlinear microwave properties of chemical vapor deposited (CVD) graphene and also established a lumped element model.8 However, lumped element models are only useful for certain sizes of structures and cannot be used for other transmission line structures To avoid this structure dependency, it is essential to characterize the intrinsic properties of graphene, such as its conductivity and relative permittivity There have been some studies on measuring the conductivity of graphene based on resonance methods that obtained results in the microwave frequency range.9,10 Unfortunately, these methods only works at certain discrete frequencies and cannot easily be used to obtain frequency-dependent conductivity properties in a broad frequency band In our previous work, the relative permittivity of graphene was determined up to GHz using a graphene-on-CPW structure.11 However, this method cannot be extended up to a Email: yuehangxu@uestc.edu.cn 2158-3226/2016/6(9)/095014/6 6, 095014-1 © Author(s) 2016 095014-2 Wu et al AIP Advances 6, 095014 (2016) the millimeter-wave frequency range due to the effects of the air gap between the graphene and transmission line Hence, the graphene permittivity and conductivity in the millimeter-wave frequency range is not available yet In this letter, the conductivity and relative permittivity of CVD graphene up to 40 GHz are reported Multilayer CPW transmission lines are properly designed as the measurement structure, with graphene loaded as one of the layers By applying the Thru-Reflect-Line (TRL) calibration, the transmission constant of the CPW and the effective permittivity of the multilayer substrate are obtained Based on the effective permittivity, the relative permittivity, conductivity and sheet resistance of graphene are extracted by employing partial capacitance techniques (PCT) The results show that as the frequency increases, the relative permittivity remarkably decreases, and these are a good fit to theoretical results The CVD graphene is fabricated on a copper foil using the method described by Li et al.12 The graphene is then transferred onto a SiO2 (300 nm)/Si(500µm, high resistivity) substrate using the PMMA-assistant method, and Raman measurements are used to confirm that the graphene is a single layer.11 To characterize the doping property of the graphene, a top gate transistor with Al2 O3 (10nm) as the gate dielectric layer is fabricated onto the SiO2 (300 nm)/Si(500 µm) substrate using photolithography The Al2 O3 is deposited using atomic layer deposition (ALD) at room temperature using a Picosun SUNALE R-200 Advanced PEALD System with Al(CH3 )3 as the metal source and oxygen plasma as the oxygen source.13 The electrodes are made of Ti(20 nm)/Au(400 nm) The drain-source current as a function of the gate voltage (Id -Vg ) for 12 àm ì àm graphene with a drain–source voltage of 5V is shown in FIG.1 The results show that the Dirac point is at Vg = 0.7 V, which means that the CVD graphene is p-type doped The jig used in our paper is based on a multilayer substrate CPW transmission line The fabrication steps are as follows: First, the standard lithographical method is used to define the regions of the coplanar waveguide after the graphene is transferred onto a SiO2 (1 µm)/Si(400 µm, high resistivity) substrate, and the graphene film outside the CPW is etched by reactive ion etching (RIE) with O2 plasma Then, a 10 nm thick layer of Al2 O3 is deposited using ALD Finally, the Ti(50nm)/Au(450nm) electrodes of the coplanar waveguide transmission line are deposited by e-beam evaporation The sample under test is loaded on the probe station and connected to the vector network analyzer (VNA) through probes and cables (shown in FIG.2) Then, the scattering parameter (S-parameter) measurements are carried out by VNA As shown in FIG.2, each test sample contains full TRL calibration structures that can be measured to determine the system errors as well as the transmission constant The transmission constant is defined as γ = α + j β, whose real part, α, is defined as the loss factor while its imaginary part, β, is defined as the phase-shift factor The dB magnitude of the transmission S-parameters (S 21 ) and the energy detected by the VNA (|S 11 |2 +|S 21 |2 ) are shown in FIG The red symbol line is the results of the sample without graphene, while the blue symbol line is the results of the sample with graphene From the dB (S21 ) results, we FIG Measured drain–source current as a function of the gate voltage (Id -Vg ) for 12 àm ì àm graphene with a drainsource voltage of 5V 095014-3 Wu et al AIP Advances 6, 095014 (2016) FIG Measurement setup and cross section of sample FIG Measured S-parameter can see that the magnitude decreased remarkably for the sample with graphene, which means that the energy transmitted from port to port decreased To determine whether the energy is reflected back to port or attenuated through the transmission line, the value of |S11 |2 +|S21 |2 is calculated As shown in FIG (insert), for the sample without graphene, approximately 50% of the energy is detected by the VNA in both ports In contrast, for the sample with graphene, only 10%-20% of the energy is detected, while 30%-40% is attenuated through the transmission line To further study the effect induced by the graphene, the loss factor is calculated based on the S-parameter results As shown in FIG 4, the loss factor of the sample with graphene is much larger than that of the sample without graphene, which indicates that the presence of graphene in the substrate of the CPW causes the transmission loss to increase The transmission constant also can be expressed as √ γ = γ0 · ε reff · µreff (1) where γ0 is the corresponding transmission constant in free space and ε reff and µreff are the effective relative permittivity and effective relative permeability, respectively In our case, whether or not the 095014-4 Wu et al AIP Advances 6, 095014 (2016) FIG Comparison of loss factor between samples with graphene and without graphene sample contains graphene, it is non-magnetic at room temperature, which indicates that for both structures, µreff = Hence, from equation (1) we can derive that !2 γ ε reff = (2) γ0 After the transmission constant is determined by the TRL calibration, the effective relative permittivity of the sample substrate can be obtained The ε reff of the samples with/without graphene canbe expressed as ε reff ε reff w/ gr w/o gr = qAl2 O3 · ε r = qAl2 O3 · ε r Al2 O3 Al2 O3 + qgr · ε r + qSi · ε r gr + qSi Si · εr + − qAl2 O3 − qSi Si + − qAl2 O3 − qgr − (3) qSi (4) Where ε reff w/o gr and ε reff w/ gr are the effective relative permittivity of the sample without graphene (sample-1) and the sample with graphene (sample-2), respectively, and ε r Al2O3 , ε r Si , and ε r gr are the relative permittivity of Al2 O3 , silicon and graphene qAl2O3 and qgr are the filling factors of Al2 O3 and graphene, respectively, and qsi and q’si are the filling factors of silicon in sample-1 and sample-2, respectively For a given structure, the filling factor can be calculated by PCT.14 From equations (3) and (4), the relative permittivity of graphene can be extracted as −q ε reff w/ gr − ε reff w/o gr − qSi Si · (ε r Si − 1) + qgr ε r gr = (5) qgr The complex relative permittivity of graphene is defined as ε r gr = ε r0 gr – j×ε r00 gr As shown in FIG.5, ε r00 gr , which corresponds to the material loss, is positive because the graphene under test is passive We can also see that ε r0 gr is negative in the entire frequency range of interest, and the absolute values of both ε r0 gr and ε r00 gr decrease with the increasing frequency The theoretical result is calculated based on the Drude model.15 Choosing the plasma frequency f P = 16.3 THz and a mean collision rate τ = 7.7 ns, the theoretical and experimental results agree with each other well As the frequency increases to 40 GHz, the value of ε r00 gr approaches 105 , while the value of ε r0 gr approaches The complex relative permittivity can also be expressed as σ ε r gr = ε r0 gr − j × (6) 2πf ε where ε is the permittivity of vacuum, with a value of 8.85 × 10-12 F/m From equation (6), the frequency-dependent bulk conductivity of graphene can be obtained from the relative permittivity, 095014-5 Wu et al AIP Advances 6, 095014 (2016) FIG Complex permittivity of CVD graphene The symbol lines represent the permittivity extracted from the measurement results, while the solid line represents the theoretical results calculated by the Drude model with the plasma frequency f P = 16.3 THz and the mean collision rate τ = 0.077 ns and the corresponding sheet resistance of the graphene can also be determined The bulk conductivity is calculated by sheet conductivity divided by the thickness of single layer graphene As the frequency increases, the conductivity is on the order of 106 and slightly decreasing, while the sheet resistance increases is 316 - 1825Ω/ (as shown in FIG.6) In this letter, we report the relative permittivity, conductivity and sheet resistance of monolayer CVD graphene up to 40 GHz Two multilayer CPW samples, one with graphene and the other without graphene, are investigated By carrying out on-wafer TRL calibration, the transmission constants of the CPWs with/without graphene are determined The results of the transmission scattering parameters and loss factors indicate that the attenuation through the CPW transmission line increases remarkably upon adding graphene into the substrate layer From the results of the transmission constants, the relative effective permittivity of the multilayer substrate is obtained Then, the relative permittivity of graphene is extracted by comparing the relative effective permittivity of the samples with and without graphene The results show the obvious frequency-dependence of the relative permittivity of graphene Finally, based on the permittivity, the conductivity and the sheet resistance of graphene are determined The conductivity is on the order of 106 S/m and decreases as the frequency increases, while the sheet resistance is on the order of 103 Ω/ and increases with the frequency The proposed method can be applied to characterize other nano-scale thickness materials Future works will extend the measurement frequency to higher frequencies, e.g., the plasma frequency FIG Conductivity and sheet resistance of CVD graphene 095014-6 Wu et al AIP Advances 6, 095014 (2016) This work is supported by the National Natural Science Foundation of China (Grant No 61474020), the Fundamental Research Funds for the Central Universities (Grant No.ZYGX2015J016) and the China Postdoctoral Science Foundation (2015T80969; 2016T90844) F Schwierz, Nature 472, 41 (2011) Park, S W Nam, M.-S Lee, and C M Lieber, Nature Mater 11, 120 (2012) S.-J Han, A V Garcia, S Oida, K A Jenkins, and W Haensch, Nature Communications 5, 3086 (2014) G Deligeorgis, M Dragoman, D Neculoiu, D Dragoman, G Konstantinidis, A Cismaru, and R Plana, 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