Graphene as broadband terahertz antireflection coating
Yixuan Zhou, Xinlong Xu, Fangrong Hu, Xinliang Zheng, Weilong Li, Penghui Zhao, Jintao Bai, and Zhaoyu Ren
Citation: Applied Physics Letters 104, 051106 (2014); doi: 10.1063/1.4863838
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View online: dx.doi/10.1063/1.4863838
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Graphene as broadband terahertz antireflection coating
Yixuan Zhou,1Xinlong Xu,1,a)Fangrong Hu,2Xinliang Zheng,1Weilong Li,1Penghui Zhao,1Jintao Bai,1and Zhaoyu Ren 1,a)
1
State Key Lab Incubation Ba of Photoelectric Technology and Functional Materials,National Photoelectric Technology,Functional Materials and Application of Science and Technology Internation
al Cooperation Center,and Institute of Photonics &Photon-Technology,Northwest University,Xi’an 710069,China 2
School of Electronic Engineering and Automation,Guilin University of Electronic Technology,Guilin 541004,China
(Received 13November 2013;accepted 18January 2014;published online 3February 2014)We examined the potential of stacked multilayer graphene as broadband terahertz (THz)antireflection coating bad on the impedance matching effect in experiment and theory.The reflected puls from the quartz and silicon substrates were obrved to change with the layer number and doping concentration of the graphene coating.Remarkable broadband impedance matching was achieved due to optimized THz conductivity.Theoretical analysis bad on Drude model and thin film Fresnel coefficients have been ud to explain the experimental phenomena,which indicated the shift of Fermi level caud by chemical doping.This work paves the way for
graphene-bad broadband THz antireflection coating.V
C 2014AIP Publishing LLC .[dx.doi/10.1063/1.4863838]
As one of the most rapid growing field,terahertz (THz)technology has stimulated many applications ranging from time-domain spectroscopy (TDS),biological imaging,high nsitive nsing,to radar and high-speed communications.1Hence,there is an urgent demand of THz devices,such as sources,detectors,and many other THz components for THz wave manipulation.2,3Among them,antireflection coatings are needed to minimize the reflections at the interfaces of the THz components,which suppress the unwanted Fabry-Perot effects.This is especially uful for the THz-TDS system,as the reflections limit the spectral resolution.
In visible-infrared region,quarter-wavelength dielectric films are the mostly ud antireflection coatings.However,they are not suitable for THz wave due to the broadband char-acteristics.Recently,impedance matching layers have been demonstrated to be a good option as antireflection coatings.Metal films,such as chromium and gold,4,5oxide micon-ductor materials,such as zinc oxide,vanadium dioxide and indium-tin-oxide,4,6,7as well as metamaterials,8have been studied as THz impedance matching layers.However,for THz applications,metal films still need to overcome the com-plexity of fabrication and high cost,oxide miconductor materials are often unstable and their effects are often insuffi-cient,and metamaterials work at narrow bandwidth.Thus,new materials with better performances are still in great demand.
Graphene as a two-dimensional atomic crystal has excellent mechanical,electrical,optical,magnetic,and ther-mal properties.9,10Particularly,the electrical and optical properties of graphene are determined by the unique Dirac cone structure with a linear dispersion relation.11,12The extraordinary carrier nature as well as the pronounced ambi-polar electric field effect have made it widely uful for the next-generation of photonics and optoelectronics.10,12In the
THz regime,the optical conductivity of graphene is deter-mined by the intraband transition and follows the Drude model.13,14What is more,efficient THz wave manipulation,such as THz modulator,switch,isolator,and polarizer,etc.,has been proved.15–18However,the impedance matching property of graphene has not been mentioned.
In this paper,we prent the impedance matching proper-ties of graphene in both theory and experiment.Graphene samples are synthesized by chemical vapor deposition (CVD),and multi-layer graphene is fabricated by layer-by-layer random stack on both quartz and silicon substrates.The lateral size of a single graphene layer is approximate 1Â1cm 2.After stacking,the overlapping area is no less than 5Â5mm 2,which is larger than the wavelength of the broad-band THz pul.Chemical doping by HNO 3can be ud to optimize the THz sheet conductivity of multilayer graphene.The am
plitude and pha of the internal reflected puls from the substrates are obrved to change with the layer number and doping concentration.After chemical doping,broadband THz-wave impedance matching can be achieved with 2-layer graphene on quartz and 5-layer graphene on silicon.Theoretical calculation with a Drude model and thin film Fresnel coefficient further suggests that the Fermi level of graphene drops from À0.11eV to À0.25eV after chemical doping.This work verifies the potential application of graphene-bad broadband THz antireflection coating.
The graphene samples were fabricated by CVD on cop-per foils as described in our previous work.19Thin poly-methyl methacrylate (PMMA)films were then spin coated on top of them.After wet-etching of the copper foils,PMMA/graphene films were transferred onto different sub-strates.Subquently,the PMMA films were dissolved with acetone.The aforementioned process were repeated N times to fabricate an N -layer graphene sample.Both quartz and high-resistivity silicon are ud as substrates,and multi-layer graphene with N ¼1,2,3,5,7is obtained in this work.This kind of randomly stacked graphene has been proved to
a)
Authors to whom correspondence should be addresd.Electronic address:xlxuphy@nwu.edu and rzy@nwu.edu.
0003-6951/2014/104(5)/051106/5/$30.00V
C 2014AIP Publishing LLC 104,051106-1
APPLIED PHYSICS LETTERS 104,051106
(2014)
be different with exfoliated one,as the electrical decoupling between layers makes it behave like isolated monolayer graphene.20–22Chemical doping was achieved by dipping the N -layer graphene/substrate into HNO 3(68%)for 5min.HNO 3is a p-type dopant in graphene.It can make electron transfer from graphene to the nitric acid and result in the shift of the Fermi level.23
Before and after the doping process,commercial THz-TDS system (Zomega Z-3)was employed to measure the THz transmission of the samples at normal incidence.In general,THz puls were generated by a photoconductive antenna under the excitation of a 100-fs lar (FemtoFiber pro NIR,TOPTICA Photonics)with a center wavelength of 790nm and the average power of 140mW at a
repetition rate of 80MHz.THz puls are detected by electro-optic sampling with a ZnTe(110)crystal.The optical path from THz generation to THz detection is purged with dried air to avoid the effect of the humidity.
Figs.1(a)and 1(b)show the measured THz signal transmitted through N -layer graphene on quartz (1mm in thickness)before and after the chemical doping process.Corresponding results for silicon substrate (0.5mm in thick-ness)are prented in Figs.1(c)and 1(d).For quartz sub-strate,the main pul appears at $8.4ps,and the reflection pul (circumscribed by a dotted window in Fig.1)appears at $21.5ps,while the main pul appears at $9.2ps and the reflection pul at $20.5ps for silicon substrate.The reflection puls are notorious limitation of spectral
resolution in THz-TDS.We focus on the reflection puls when the layer number increas.With layer number increasing,the reflection pul is obrved to suppress at 3-layer for quartz substrate (Fig.1(a))and at 7-layer for sili-con substrate (Fig.1(c)).After chemical doping,the sup-pression appears at 2-layer for quartz substrate (Fig.1(b))and 5-layer for silicon substrate (Fig.1(d)).All the are due to the impedance matching properties from graphene layer.In particular,for uncoated substrate,the reflection pul has a valley-peak shaped resonance,which is weak-ened by graphene for all conditions.We also obrved the polarity reversal of the reflection puls as shown in Figs.1(a)
,1(b),and 1(d),due to the pha change of the imped-ance matching layer.
We prent a propagation model to analyze the effect as shown in Fig.2.Pul 1reprents the main pul and pul m (2,3,4…)reprents the reflection pul.N -layer gra-phene is placed at the interface between air and substrate (d sub in thickness)with refractive indices n 1¼n air and n 3¼n sub .Graphene is a two-dimensional material with a thickness d gra %0.335nm.24Thus even when N ¼30,the film is sub-10nm and much thinner than the skin depth of THz wave.Therefore,it can be treated as a zero-thickness conductive film with the transmission and reflection at the interface given by 5
t gra ¼2n 1
n 1þn 3þZ 0r total ;
(1)r gra ¼
n 3Àn 1ÀZ 0r total
130total
ideal是什么意思
;
(2)
where Z 0¼377X is the impedance of free space and r total the optical sheet conductivity of N -layer graphene.
The Fresnel coefficients t ij ¼2n i =ðn i þn j Þand r ij ¼ðn i Àn j Þ=ðn i þn j Þare ud to describe the transmission and reflection at the interface between air and the substrate.At normal incidence,the transmission coefficient of the m -th pul can be expresd as follows:
t ðm Þ¼
身份证查六级成绩E tm ðx ÞE THz ðx Þ
¼t gra t 34r m À1gra r m À1
34p air
Âðx ;Àd sub Þ½p sub ðx ;d sub Þ 2m À1;
(3)
FIG.1.Transmitted THz puls through (a)N -layer (1,3,5,7)graphene on quartz before doping;(b)N -layer (1,2,5,7)graphene on quartz after doping;(c)N -layer (1,3,5,7)graphene on silicon before doping;and (d)N -layer (1,3,5,7)graphene on silicon after doping.The results of uncoated substrates are shown as references
(ref.).FIG.2.Schematic of THz pul propagation through N -layer graphene on substrate (quartz or silicon).The incident THz pul and the main transmit-ted pul (pul 1)are indicated by red color,while the internal reflections in the substrate are blue,with only the first two puls (puls 2and 3)shown.
where x is the angular frequency;E THz,E tm are electric fields of the incident and transmitted THz waves; and p airðx;Àd subÞ¼exp i x d sub n air=c
ðÞand p subðx;d subÞ¼expÀi x d sub n sub=c
ðÞare propagation factors in air and the substrate.The corresponding transmission coefficient of
uncoated substrate is defined as tðmÞ
catchonsub ,which shows a similar
expression as Eq.(3)by replacing t gra and r gra to t13and r31.
For pul1(m¼1),tð1Þis in direct proportion to t gra and inverly proportional to the optical sheet conductivity of N-layer graphene.Differently,tð2Þis proportional to r gra besides t gra,which is intrinsic related to optical sheet conductivity of the coated layer.
It implies that the internal reflection can significantly be reduced by decreasing the impedance mismatch.When the THz wave travels from the substrate to air(n3>n1),the pha of pul2will be dominated by r total(Eq.(2)).When r total<ðn3Àn1Þ=Z0(r gra>0),pul2has the same pha as the incident pul.When r total>ðn3Àn1Þ=Z0(r gra<0), pul2shows a p pha shift.When r total¼ðn3Àn1Þ=Z0 (r gra¼0),impedance matching condition can be achieved and the reflection is suppresd.The amplitude and pha of the reflection can be controlled by the sheet conductivity of the coated graphene-layer.
As a qualitative analysis,Fig.1can be explained as fol-lows.Firstly,the optical sheet conductivity ris with the graphene layer number increasing,the proportional relation-ship with main pul leads to the reduction of the amplitude in all conditions.Secondly,when pul2is suppresd,it means impedance matching condition is approaching ful-filled.Similarly,when pul2shows a p pha shift,it sug-gests the conductivity of the stacked graphene is beyond the impedance matching value.Specifically,3-layer and2-layer graphene on quartz before and after doping,7-layer and5-layer graphene on silicon before and after doping in experi-ments,are most approximative to the impedance matching condition,respectively.Thirdly,as proved in previous works,18,23,25the chemical doping by HNO3improves the optical sheet conductivity of graphene on either quartz or sil-icon.It leads to opti
mize impedance matching condition due to the increasing conductivity.Lastly,as the refractive index of quartz(n quartz¼1.955)is much lower than the refractive index of silicon n silicon¼3.42,the impedance matching con-dition is easier to achieve on quartz than on silicon.
We define the amplitudes of the transmission through substrate and N-layer graphene/substrate for the m-th pul
as AðmÞ
NÀlayer and AðmÞ
ref
in frequency domain,which have a rela-
tionship with the transmission coefficients tðmÞ=tðmÞ
sub ¼AðmÞNÀlayer=AðmÞref.Combined with Eqs.(1)–(3),optical sheet conductivity can be simplified from pul1:
r total¼n1þn3
Z0
Að1Þ
ref
A
NÀlayer英文邀请信
À1
@
1
A:(4)
The calculated THz sheet conductivity of graphene is shown in Fig.3,which isflat and featureless from0.2to1.2THz, consistent with the previous results.13,14,21The nearly con-stant THz conductivity leads to a broadband respon as applications.For quartz,the impedance matching sheet con-ductivi
ty is calculated to be2.53mS with n quartz¼1.955.Before doping,the average sheet conductivity values of1,3, 5,7-layer graphene are approximate0.6,2.0,3.2,and4.8mS, thus the perfect impedance matching is expected to occur between3and5layers.After doping,the average optical sheet conductivities for1,2,5,7-layer graphene are around 1.0,3.2,7.2,and10.5mS,and the ideal impedance matching layer number reduces to between1and2.For silicon,the im-pedance matching sheet conductivity is calculated to be6.42 mS with n silicon¼3.42.Before doping,the average optical sheet conductivities of1,3,5,7-layer graphene are about1.0, 1.5,2.8,and5.7mS,and the ideal impedance matching con-dition cannot be reached even with layer number7.After doping,the average optical sheet conductivities become around1.8,4.4,7.1,and11.7mS and5-layer graphene has the optimized sheet conductivity as shown in Fig.1.
We begin the discussion with the optical sheet conduc-tivity of N-layer graphene.In THz region where intraband transitions dominate,the optical conductivity of monolayer graphene follows a Drude model.14,15,26In consideration of the carrier density dependence,the intraband conductivity has a full description as follows:14
r gðxÞ¼
2e2k B T
p h2ðCÀi xÞ
ln expÀ
E F
2k B T
þexp
E F
2k B T
;
(5) where e and h are the elementary charge and Planck con-stant.T and k B are the temperature and Boltzmann constant.
C and E F are the scattering rate and the Fermi energy.The Fermi energy is related to the carrier density N c by E F¼6 h v F
ffiffiffiffiffiffiffiffiffiffiffi
p j N c j
p26
with negative(positive)corresponds to hole(electron)doping.v F¼1:1Â106m=s is the Fermi ve-locity.Room temperature T¼300K can be t to a constant. Therefore,the optical conductivity of monolayer graphene depends on the frequency,the quality of the sample(C),and the carrier density(or Fermi energy)as suggested in Eq.(5). With the same fabrication method,C can be expected to
be FIG.3.THz sheet conductivity obtained from pul1for(a)N-layer(1,3,5,7) graphene on quartz before doping;(b)N-layer(1,2,5,7)graphene on quartz after doping;(c)N-layer(1,3,5,7)graphene on silicon before doping;and(d)N-layer (1,3,5,7)graphene on silicon after doping.
constant.The conductivity is almost frequency independent in THz frequency range.Therefore,the carrier density becomes the key issue to tune the sheet conductivity with graphene.However,although the electrons and holes can be tuned up continuously in concentration as high as 1013cmÀ2,9it still cannot match the requirement of imped-ance matching with high refractive index substrate,such as silicon.Therefore,stacked multilayer graphene combined with chemical doping method is expected in order to opti-mize the THz sheet conductivity.
It has been demonstrated that the THz wave absorption of multilayer graphene has a strong dependence on the stacking arrangements and misorientation angles between layers.22However,randomly stacked sample shows an elec-tronically decoupling,which makes it behave like isolated monolayer graphene.20In THz regime,this conclusion has been further testified by THz-TDS.21The transmission coef-ficient of multilayer graphene can be calculated with a layer-by-layer model ud in previous works,21,24in which the multilayer graphene is regarded as homogeneous dielec-tric layer with a thicknessðNÀ1Þd gra.We assume all the graphene layers have
the same scattering rate and the same Fermi energy for simplicity.Thus,the relationship between the optical sheet conductivity of the N-layer(N>1)sample and the monolayer graphene can be obtained combined with Eq.(1)as follows:
rðNÞtotal ¼½ðM1ÀM2Þexpðik g d graÞþðM3ÀM4ÞexpðÀik g d graÞ
ðn1þZ0r gÞðn3þZ0r gÞ
2Z0
ffiffiffiffie
g
p
merry
þ½ðM1þM2Þexpðik g d graÞþðM3þM4ÞexpðÀik g d graÞ
n1þZ0r g
2Z0
þ½ðM1ÀM2Þexpðik g d graÞÀðM3ÀM4ÞexpðÀik g d graÞ
n3þZ0r g
2Z0
þ½ðM1þM2Þexpðik g d graÞÀðM3þM4ÞexpðÀik g d graÞ
ffiffiffiffie
g
p
2Z0
À
n1þn3
Z0
;
(6)
where k g¼x
ffiffiffiffie
g
p
=c is the propagating vector in graphene,and the coefficients M1,M2,M3,and M4have the following expres-
sion as follows:
M1 M3M2 M4
¼
1þ
Z0r g
2
ffiffiffiffie
g
p
!
expðik g d graÞ
À
Z0r g
2
ffiffiffiffie
g
p expðik g d graÞ
Z0r g
2
你也一样英语怎么说ffiffiffiffie
g
p expðÀik g d graÞ
1À
youdaofanyi
Z0r g
2
ffiffiffiffie
g
p
!
expðÀik g d graÞ
B B
B B
@
1
C C
C C
A
NÀ2
:
(7)
We define the relative amplitude transmission for THz
pul m as AðmÞ
NÀlayer =Að1Þ
ref
.The theoretical calculated relative
amplitude with parameter C¼100cmÀ1,combined with the corresponding experimental data,is shown in Fig.4.The ex-perimental data at0-layer in Fig.4reprent the relative amplitudes of pul2for uncovered substrates.The clo matching of the experiments and theoretical calculation con-firms the tunability of impedance matching with graphene layer.For quartz,the relative amplitude transmission of pul2is0.104.Before doping,the experimental data show the relative amplitude transmission of pul2can be sup-presd to0.028with3-layer graphene and further reduced to0.013with4-layer one in theory.After doping,the relative amplitude transmission of pul2can be suppresd to 0.0025,a little higher than the theoretical calculated0.017. As suggested from Eq.(5),t
he Fermi energy drops from À0.11toÀ0.25eV after chemical doping.It also suggests that the samples before chemical doping are also slightly hole-doped by the substrate or the transfer process,which has been confirmed in some previous works.14,15,26For sili-con,the relative amplitude of pul2can reach0.300. Before doping,the ideal impedance matching condition cannot be reached even with7-layer graphene.After doping, 5-layer graphene can be ud as antireflection layer with a suppresd relative amplitude as low as0.028.The Fermi energy in the theoretical model from Eq.(5)also drops from À0.11eV toÀ0.25eV.
The results suggest the reflection properties of the substrate can be changed by the layer number of graphene and impedance matching can be achieved with suitable layers.Furthermore,chemical doping is proved to be a good solution to drive the Fermi level down,which will greatly optimize impedance matching properties of graphene layer. The combination provides a simple and effective method to fabricate graphene-bad broadband THz antireflection coating.From Fig.4,the decrea in main puls in ampli-tudes suggests that graphene still cannot overcome the draw-back of absorption loss as obrved in metallic layers.4,5 However,graphene is still superior than metal and micon-ductor as THz impedance matching layer.Due to the high THz conductivity,graphene is more suitable for substrates with high refractive index,when the impedance matching layer might be too thick to fabricate with metal and mi-conductor.Compared with metal,5graphene also has
