DOC

Spin-Polarized

By Jose Thompson,2014-02-18 22:30
9 views 0
Spin-PolarizedSpin

    Spin-Polarized

    Commun.Theor.Phys.(Beijing,China)54(2010)PP.741746

    ?ChinesePhysicalSocietyandIOPPublishingLtdVo1.54,No.4,October15,2010 Spin.PolarizedCarriersInjectionfromFerromagneticMetalintoOrganic Semiconductor

    QIAOShiZhu(乔士柱),ZHAOJunQing(赵俊卿),tJIAZhen-Feng(贾振

    ),andZHANGTianYou(张天佑)

    SchoolofScience,ShandongJianzhuUniversity,Jinan250101,China

    (ReceivedJanuary4,2010;revisedmanuscriptreceivedFebruaryl,2010) AbstractChargecarriersinorganicsemiconductoraredifferentfromthatoftraditionalinorganicsemiconductor.

    Basedonthree-currentmode1.consideringelectrical

    eldeffect.wepresentatheoreticalmodeltodiscussspin-polarized

    injectionfromferromagneticelectrodeintoorganicsemiconductorbyanalyzingelectrochemicalpotentialbothjnfer-

    romagneticelectrodeandorganicsemiconductors.Thecalculatedresult0ftismodelshowseffectsofelectrode'sspin

    polarization,equilibriumvalueofpolaronsratio,interracialconductance,bulkconductiviofmaterialsandelectrical

    field.Itjsfoundthatwecouldgetdecentspinpolarizationwithcommonferromagneticelectrodebyincreasingequi

    libriumvalueofPolaronsratio.V

    ,ealsofindthatlargeandmatchedbulkconductivityoforganicsemiconductorand electrode.smaljspindependentinterfacialconductance,andenoughlargeelectrical

    eldarecriticalfactorsforincreasing

    spinpolarization.

    PACSnumbers:72.25.Hg,72.25.Mk,

Keywords:spin-polarizedinjection

    72.80.Le

    organicsemiconductor,polaron

    1Introduction

    SemiconductordevicesbasedonmaniDulationof electron'sspinhaverecentlyattractedconsiderable attention.[1-4Inspindevices.semiconductorisusually nonmagnetic,thusspin-polarizedinjectionandtrans

    portinsemiconductorsandheterostructuresplayade

    terminantroleindesignofnewspindevices.L5JCom

    paredwithconventionalsemiconductors,organicsemi

    conductors(OSCs)havelongerspindiffusionlength,[71so

    theyaremuchsuitableforspin-polarizedtransportation. Dediueta1.firstreportedroomtemperaturespininjec

    tionintoOSCsin2002.TheyappliedLao7Sr0.

    3MnO3

    (LSMO1tosexithieny1.andfoundamagnetoresistance effectofupto30%.Xiongeta1.alsoobservedspininjec

    tionandtransportwithstructureofLSMO/Alq3/Co._9_ Fortheoreticalconsideration,wetookchargecarriersin 0SCaselectronsandholes.lJHowever.0SCsaredif-

    ferentfrominorganicsemiconductor.Theirflexibilityin- duceschargecarrierstobecompositeparticlesofelec

    tronswithinterna1structurescharacterizedbylattice distortions,suchaschargedspinpolaronsandspinless bipolarons.n1r2lReneta1.consideredthedifierenceand suggestedathreecurrentmodell13Jtodescribethespin

    polarizedcarriertransportinOSCs.Intheirmode1.elec

    tricalfieldeffectwasnottakenintoconsideration.Infact,

electricalfieldasstrongas104^100V/cmusuallyexists

    inspindevices,suchasspinpolarizedorganiclightemit

    ringdevicefS0LED1.Maeta1.introducedamodeltoil- luminatetheinfluenceofelectricalfield.l4JIntheirmodel

    theOSCwastakenashighlydegeneratesystem.Consid

    eringthatnon??degeneracyisindispensabletotheappear-- anceofpolaronsandbipolaronsin0SCs.inthispaper.we developathreecurrentmodelonbasisofnondegeneracy

    andhighelectricalfield,anddiscussspinpolarizedinjec

    tionofcarriersfromferromagneticelectrodeinto0SCs. 2Model

    E

    —————————————

    ?

    0SC

    O

    FM

    Fig.1SchematicpictureofOSC/FMstructure.Spin polarizedelectronsareinjectedfromFMintoOSC.The electricalfieldandthereforetheelectricalcurrentarepar

    alleltoaxis.

    Weconsideronedimensionalspininjectionsystem

    thatcomprisesasemiinfiniteOSC(X<0)andasemi

    infiniteferromagneticmetal(FM)(x>0).Spinpolarized

    electronsinFMareinjectedintoOSC.TheiI1jectedelec

    tronsaresupposedtoconvertcompletelyintopolarons SupportedbytheNaturalScienceFoundationofShandongProvinceunderGrantNo.Y2006

    A18andtheKeyProgrammeofNature

    FoundationofShandongJianzhuUniversityunderGrantNo.XZ050102

    tCorrespondingauthor

,E-mail:jqzhao05@126.com

    742QIAOShiZhu,ZHAOJunQing,JIAZhenFeng,andZHANGTian

    YouVb1.54

    andbipolarons.Somespin-upelectronscombinewiththe sameamountspin-downelectronstoformbipolarons,and theotherelectronschangeintopolaronswithaccordant spins.ThereforetherearethreechannelsinOSCforspin

    uppolarons,spin-downpolarons,andspinlessbipolarons, respectively.Thewholetransportpictureisschematically showninFig.1.

    Theelectricalcurrentofspin一叼(=T,)polaronsin

    OSCcouldbeexpressed[i5]as

    Jp=pE(-e)DOnpn(1)

    where,Dstandforconductivityanddiffusionconstant, subscriptPmeanspolarons,pstandsforconcentration

    deviationofspin-~polaronsfromitsequilibriumvalue p0

    .Thebipolaronsaresupposedstable,andthusthe transitionbetweenpolaronsandbipolaronsisneglected, then

    pT+p=0

    Differentialequationofpolarons'concentrationcould beexpressedas[6

    p

    Ot——.

    n

    ......

    p..

    n

    4-.n

......

    p..

    o———

    Ojpq/Ox

    q

    (#pT)

    wherestandsforspinrelaxationtime,meanstheop-

    positespinof.

    TheelectricalcurrentacrossthesystemobeysOhm'S 1aw[17

    J=O-pnOq#pn

    ,

    whereistheelectrochemicalpotential,p= (礼卵十凡p_,Je/gp,wherestandsformobility.Consider- ingconcentrationischangingwithposition,usingEqs.(1) and(4)wehave

    n(+)(5)

    whereCiSanintegralconstant,Einsteinrelation ep/=[innondegeneratesystemisused,and spindependenceofmobilityanddiffusionconstantisne- glected.

    Definingspinpolarizedconcentrationps=ptnpl

    inOSC.wehaveB9]

    npsx)(exp(),<0,(6)

    whereLListhespindiffusionlengthincludingelectrical field.

    Equations(2),(5),and(6)give

    eE+.

    (:n

    ps(0)

~

    x)+Equations(1)and(6)give

    jps抽一Jp$~nps(0)ep()nps(0)

    Currentdensityofpolaronscouldbeexpressedas

    3pT

    exp

    ()

    TeEupn~

    +e(+))eXp()

    TeEupn~p

    e

    (+)(0)exp()

    ContrastingtoEqs.(1),(3),and(4)inOSC followingEqs.(11),(12),and(13)validinFM JE+e,

    On

    I

    nOIOjn

    /Oz

    Ot'7_'.

    J=.

    wehave

    (11)

    (12)

    InFM,nnq,soitcouldbeacceptablethat ;:n+qdoesnotchangewithposition.Considering

    Einsteinrelation:q2Dq?andNT/7-T/tf21

    inFM,whereNisdensityofstates,usingEqs.(11),(12),

    (8)

    (10)

and(13)wehave

    =

    1

    D

    (0t7Itl Ox2=

    1(#

    l--#TD7-) ll

    \/

    SolvingEq.(14)gives

    (:)=exp(-x/(

    (14)

    +ejx(15) whereLisspindiffusionlengthinFM,Cisanintegral

    constant. 0p

    n

    E

    e

    :

    

    p

    .1

    +

    T

    p

    .n

    ll

    p

.n

    ?l

    g

    ,l,

    9

    /,

    d

    n

    a

    ,l,8

    ,,

    S

    n

    O

    .1t

    a

    U

    q

    B

    No.4SpinPolarizedCarriersInjectionfromFerromagneticMetalintoOrganicSemiconductor743

    Equations(13)and(15)give

    :卉一九:exp(/L)+J3/I7sI7TI7一—AL.xp

    where(o-T)/(T+)isspinpolarizationofFM. Ifinjectedspin?-downelectronsallconvertintobipo?-

    larons,polaronsratioofinjectedchargecarriers5=

    23/(1+),whileinjectedspindownelectronallconvert intopolarons,5=1,soingeneral,2fl/(1+)51. Assuming=np06

    p

0+no

    p),thenfor723/(1+),

    isdeterminedbyOSC,and=7,whilefor7< 23/(1+),isdeterminedbyFM,and=23/(1+). Weassumethatthereisnospin-flipscatteringatthe OSC/FMinterface,thenbothchargeandspincurrents arecontinuousacrosstheinterface,sowehave jd0+):Jp(0~)

    jp,(0十上

    whereGisinterfacialconductance,and:n/n When

    ,

    2

    <=-o.

    Equations(7),f8),f10),f15),f16),and(17)give [(27)/7][23/(1~32)](1/)(1/2)(1/0TG$1/O+G+)

    (eE/2+kBT/2LL)[(1/OTGT+1/O,G+)+4/(1)(1/a)L+(2keT/cro)[(2)/J

    P(0)=23

    ,

    whereP(0)=ps(0)/(np+nbp)isspinpolarizationof polarons'concentrationattheinterface,o-=t+Iis conductivityofFM,and.isconductivityofOSC.The

    concentrationspinpolarizationofpolaronsdecreasesex- ponentiallywithpositioninOSC.whichcanbefoundin Eq.(6),thereforeformP(0).UsingEq.(18)wecanana

    lyzethemagnitudeofspin-polarizedinjectionintoOSC. 3ResultandDiscussion

    ThedependenceofP(O)onisshowninFig.2.We canseethatwhen7/(2),therelationbetween

    P(0)and7varieswith:when=0.5,P(0)increases

withtheincreasingof,butwhen=0.6and:0.7,

    P(O)decreaseswiththeincreasingof7,whichisconsist withourpreviouswork.17_When>7/(2,y),P(0)

    doesnotchangewithaccordingtoEq.(18),whilethe increasingofleadstoobviousincreasingofP(0).In ourpreviouswork.[wedidnottakethecircumstanceof

    >7/(2~7)intoconsideration,sowejusthadfractional result.Whythereispolaronsconcentrationpolarization inOSCwhen=O?Itmaybederivedfromdepen

    denceofpolaronratioonmaterialsaswellasexternal circumstancesuchastemperatures,electricalfield[22]and probablythespinpolarizationofinjectionelectrons. ThedependenceofP(0)onelectricalfieldisshown inFig.3,wheretheleftpanelstandsfor7/(2~7)

    andtherightpanelstandsfor>7/(27).Itisfound

    thatP(o)increasesrapidlywiththeincreasingofelectrical fieldwhenE<100V/m.WhenE>100V/m.P(O1does notincreaseremarkablywiththeincreasingofelectrical field.Wecanseefromtherightpanelthatlargefa- vorsP(0),butcommonferromagnetsFe,Co,andNihave (18)

    spinpolarizationbetween40%and50%.Mostreportsof spin-polarizedinjectionintoorganicfilmhaveusedLSMO duetoitsreported100%spinpolarization.Hereforthe leftpanel,whenE>10V/m,P(0)increaseswiththe increasingof,sowecangetdecentP(0)withcommon FMbyincreasingandelectricalfield.

    Fig.2Calculationoftheconcentrationspinpolariza- tionofpolaronsattheinterfaceversus,yfordifferent spinpolarizationofelectrode.T=300KIL=100nm,

Report this document

For any questions or suggestions please email
cust-service@docsford.com