双层石墨烯的到点特性和透光特性

Optical conductance and transmission in bilayer graphene

H. M. Dong, J. Zhang, F. M. Peeters, and W. Xu

Citation: J. Appl. Phys. 106, 043103 (2009); doi: 10.1063/1.3200959

View online: http://dx.doi.org/10.1063/1.3200959

View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v106/i4

Published by the American Institute of Physics.

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Downloaded 22 Dec 2012 to 140.124.249.101. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissionsOpticalconductanceandtransmissioninbilayergraphene

H.M.Dong,1J.Zhang,2F.M.Peeters,3andW.Xu1,2,a͒1KeyLaboratoryofMaterialsPhysics,InstituteofSolidStatePhysics,ChineseAcademyofSciences,Hefei230031,China2DepartmentofPhysics,YunnanUniversity,Kunming610015,China3DepartmentofPhysics,UniversityofAntwerp,Groenenborgerlaan171,B-2020Antwerpen,Belgium

͑Received5May2009;accepted10July2009;publishedonline20August2009͒

Wepresentatheoreticalstudyoftheoptoelectronicpropertiesofbilayergraphene.Theoptical

conductanceandtransmissioncoefficientarecalculatedusingtheenergy-balanceequationderived

fromaBoltzmannequationforanair/graphene/dielectric-wafersystem.Forshortwavelengths͑␭Ͻ0.2␮m͒,weobtaintheuniversalopticalconductance␴=e2/͑2ប͒.Interestingly,thereexistsan

opticalabsorptionwindowinthewavelengthrange10–100␮m,whichisinducedbydifferent

transitionenergiesrequiredforinter-andintra-bandopticalabsorptionsinthepresenceofthe

Moss–Bursteineffect.Asaresult,thepositionandwidthofthisabsorptionwindowdepend

sensitivelyontemperature,carrierdensity,andsamplemobilityofthesystem.Theseresultsare

relevantforapplicationsofrecentlydevelopedgraphenedevicesinadvancedoptoelectronicssuch

astheinfraredphotodetectors.©2009AmericanInstituteofPhysics.͓DOI:10.1063/1.3200959͔

I.INTRODUCTION

Grapheneisthebasisofanewclassofnanostructures

whereconductionoccursinsingleorfewlayersofcarbon

atomsarrangedinahexagonallattice.1Owingtoitsunique

electronicbandstructureandthecorrespondingquasirelativ-

isticfeatures,graphenehasattractedagreatattentioninre-

centyears.Furthermore,graphenecanhaveahighcarrier

densityandexhibitshighelectronicmobilityevenatroom

temperature.Oneofthemajoradvantagesofagraphenede-

viceisthatthecarrierdensityinthegraphenelayercanbe

controlledveryeffectivelythroughagatevoltage.1Hence,

graphenehasbeenproposedasa“buildingblock”forad-

vancedelectronicdevices2suchasgraphenep-nandp-n-p

junctions,3transistors,4etc.Inrecentyears,thestudyofthe

electronictransportpropertiesofDiracquasiparticlesin

graphenehasrapidlybecomeanimportantresearchtopicin

nanomaterialscience,condensedmatterphysics,and

nanoelectronics,5whichispartlymotivatedbythepossible

applicationsofgrapheneinadvancedelectronicdevices.6

Recently,theopticalandoptoelectronicpropertiesofdif-

ferentgraphenesystemshavebeeninvestigated.Inparticu-

lar,itwasfoundexperimentallythattheopticalconductance

pergraphenelayerisgivenbyauniversalvalue␴

=e2/͑4ប͒inthevisiblefrequencyandUVrange.7Asacon-

sequence,thelighttransmittanceofmonolayerandbilayer

graphenedevicesareabout0.98and0.96,respectively,inthe

visiblebandwidth.8Thisimportantdiscoveryhasresultedin

theproposalthatgraphenecanbeusedtoreplaceconven-

tionalindiumtinoxideelectrodesformakingbetterand

cheaperopticaldisplays.9Kuzmenkoetal.7recentlyfound

experimentallythatforphotonenergysmallerthan0.2eV,

thereisanopticalabsorptionwindow.Thewidthanddepth

ofthiswindowdependstronglyontemperature.Thisinter-

estingfindingimpliesthatgraphenemayalsobeappliedforinfrareddetectioninambientcondition.Veryrecentexperi-

mentalworkshowedthatgraphenecanhavestrongintra-

andinter-bandtransitionswhichcanbesubstantiallymodi-

fiedthroughelectricalgating,similartoresistancetuningin

graphenefield-effecttransistors.10Theseexperimentalresults

showclearlythatgraphenecanbeusednotonlyasadvanced

electronicdevicesbutalsoasopticaldevicesforvariousap-

plications.

Inconjunctionwithexperimentalinvestigationsintoop-

toelectronicpropertiesofgraphenesystems,theoreticalstudy

inthisareahasbeenquiteactive.Theuniversalopticalcon-

ductanceinthevisibleregime,␴0=e2/4បpergraphenelayer,

hasbeenobtainedtheoretically.7,11Thefeaturesofgraphene

systemsunderfar-infrared͑FIR͒orterahertzradiationhave

alsobeeninvestigatedtheoreticallyusingvarious

approaches.12,13Theresultsobtainedfromthesetheoretical

investigationshaveindicatedthat͑i͒intheshortwavelength

suchasvisibleregime,inter-bandtransitionistheprincipal

channelforopticalabsorptionandconductancein

graphene;7,11͑ii͒intheFIRorterahertzbandwidth,both

inter-andintra-bandtransitionsplayimportantrolestocause

opticalabsorptionandconductanceingraphene;12,13and͑iii͒

theoptoelectronicpropertiesforgrapheneintheFIRortera-

hertzregimedependstronglyontemperatureandcarrierden-

sityinthesystem.12

Theopticalandoptoelectronicpropertiesofmonolayer

graphenehasbeenwelldocumented.7,8,10Incontrasttoa

nearlylinearenergyspectruminmonolayergraphene,bi-

layergraphenehasaquadraticenergyspectruminlowen-

ergyregime.14,15Thus,thedensityofstatesinabilayer

graphenesystemdifferssignificantlyfromthatinmonolayer

graphene.Ithasbeenrealizedthatbilayergrapheneisof

equalimportanceasmonolayergrapheneforbothtechno-

logicalapplicationsandfundamentalscience.4,16Inthispa-

perwepresentadetailedtheoreticalstudyoftheoptoelec-

tronicpropertiesofbilayergraphene.InSec.II,the

theoreticalapproachisdevelopedtocalculatetheoptoelec-a͒Electronicmail:wenxu_issp@yahoo.cn.JOURNALOFAPPLIEDPHYSICS106,043103͑2009͒

0021-8979/2009/106͑4͒/043103/6/$25.00©2009AmericanInstituteofPhysics106,043103-1

Downloaded 22 Dec 2012 to 140.124.249.101. Redistribution subject to AIP license or copyright; see http://jap.aip.org/about/rights_and_permissions